Aljabar Contoh

$f (x) = b {(x + a)}^{3} + c$

Langkah 1

Tuliskan $f (x) = b {(x + a)}^{3} + c$ sebagai sebuah persamaan.

$y = b {(x + a)}^{3} + c$

Langkah 2

Saling tukar variabel.

$b = y {(x + a)}^{3} + c$

Langkah 3

Selesaikan $y$ .

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Langkah 3.1

Tulis kembali persamaan tersebut sebagai $y {(x + a)}^{3} + c = b$ .

$y {(x + a)}^{3} + c = b$

Langkah 3.2

Kurangkan $c$ dari kedua sisi persamaan tersebut.

$y {(x + a)}^{3} = b - c$

Langkah 3.3

Bagi setiap suku pada $y {(x + a)}^{3} = b - c$ dengan ${(x + a)}^{3}$ dan sederhanakan.

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Langkah 3.3.1

Bagilah setiap suku di $y {(x + a)}^{3} = b - c$ dengan ${(x + a)}^{3}$ .

$\frac{y {(x + a)}^{3}}{{(x + a)}^{3}} = \frac{b}{{(x + a)}^{3}} + \frac{- c}{{(x + a)}^{3}}$

Langkah 3.3.2

Sederhanakan sisi kirinya.

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Langkah 3.3.2.1

Batalkan faktor persekutuan dari ${(x + a)}^{3}$ .

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Langkah 3.3.2.1.1

Batalkan faktor persekutuan.

$\frac{y {(x + a)}^{3}}{{(x + a)}^{3}} = \frac{b}{{(x + a)}^{3}} + \frac{- c}{{(x + a)}^{3}}$

Langkah 3.3.2.1.2

Bagilah $y$ dengan $1$ .

$y = \frac{b}{{(x + a)}^{3}} + \frac{- c}{{(x + a)}^{3}}$

Langkah 3.3.3

Sederhanakan sisi kanannya.

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Langkah 3.3.3.1

Pindahkan tanda negatif di depan pecahan.

$y = \frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}$

Langkah 4

Replace $y$ with $f^{- 1} (b)$ to show the final answer.

$f^{- 1} (b) = \frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}$

Langkah 5

Periksa apakah $f^{- 1} (b) = \frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}$ merupakan balikan dari $f (b) = b {(x + a)}^{3} + c$ .

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Langkah 5.1

Untuk memverifikasi balikannya, periksa apakah $f^{- 1} (f (b)) = b$ dan $f (f^{- 1} (b)) = b$ .

Langkah 5.2

Evaluasi $f^{- 1} (f (b))$ .

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Langkah 5.2.1

Tulis fungsi hasil komposit.

$f^{- 1} (f (b))$

Langkah 5.2.2

Evaluasi $f^{- 1} (b {(x + a)}^{3} + c)$ dengan mensubstitusikan nilai (Variabel1) ke dalam (Variabel2).

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b {(x + a)}^{3} + c}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}$

Langkah 5.2.3

Sederhanakan pembilangnya.

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Langkah 5.2.3.1

Gunakan Teorema Binomial.

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b (x^{3} + 3 x^{2} a + 3 x a^{2} + a^{3}) + c}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}$

Langkah 5.2.3.2

Terapkan sifat distributif.

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b x^{3} + b (3 x^{2} a) + b (3 x a^{2}) + b a^{3} + c}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}$

Langkah 5.2.3.3

Sederhanakan.

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Langkah 5.2.3.3.1

Tulis kembali menggunakan sifat komutatif dari perkalian.

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b x^{3} + 3 b x^{2} a + b (3 x a^{2}) + b a^{3} + c}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}$

Langkah 5.2.3.3.2

Tulis kembali menggunakan sifat komutatif dari perkalian.

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b x^{3} + 3 b x^{2} a + 3 b x a^{2} + b a^{3} + c}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}$

Langkah 5.2.4

Sederhanakan suku-suku.

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Langkah 5.2.4.1

Gabungkan pembilang dari penyebut persekutuan.

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b x^{3} + 3 b x^{2} a + 3 b x a^{2} + b a^{3} + c - c}{{(a + x)}^{3}}$

Langkah 5.2.4.2

Gabungkan suku balikan dalam $b x^{3} + 3 b x^{2} a + 3 b x a^{2} + b a^{3} + c - c$ .

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Langkah 5.2.4.2.1

Kurangi $c$ dengan $c$ .

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b x^{3} + 3 b x^{2} a + 3 b x a^{2} + b a^{3} + 0}{{(a + x)}^{3}}$

Langkah 5.2.4.2.2

Tambahkan $b x^{3} + 3 b x^{2} a + 3 b x a^{2} + b a^{3}$ dan $0$ .

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b x^{3} + 3 b x^{2} a + 3 b x a^{2} + b a^{3}}{{(a + x)}^{3}}$

Langkah 5.2.4.3

Sederhanakan pernyataannya.

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Langkah 5.2.4.3.1

Pindahkan $x^{2}$ .

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b x^{3} + 3 b a x^{2} + 3 b x a^{2} + b a^{3}}{{(a + x)}^{3}}$

Langkah 5.2.4.3.2

Pindahkan $b$ .

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b x^{3} + 3 a b x^{2} + 3 b x a^{2} + b a^{3}}{{(a + x)}^{3}}$

Langkah 5.2.4.3.3

Pindahkan $x$ .

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b x^{3} + 3 a b x^{2} + 3 b a^{2} x + b a^{3}}{{(a + x)}^{3}}$

Langkah 5.2.4.3.4

Pindahkan $b$ .

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b x^{3} + 3 a b x^{2} + 3 a^{2} b x + b a^{3}}{{(a + x)}^{3}}$

Langkah 5.2.4.3.5

Susun kembali $b$ dan $a^{3}$ .

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b x^{3} + 3 a b x^{2} + 3 a^{2} b x + a^{3} b}{{(a + x)}^{3}}$

Langkah 5.2.4.3.6

Pindahkan $b x^{3}$ .

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{3 a b x^{2} + 3 a^{2} b x + a^{3} b + b x^{3}}{{(a + x)}^{3}}$

Langkah 5.2.4.3.7

Pindahkan $3 a b x^{2}$ .

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{3 a^{2} b x + a^{3} b + 3 a b x^{2} + b x^{3}}{{(a + x)}^{3}}$

Langkah 5.2.4.3.8

Susun kembali $3 a^{2} b x$ dan $a^{3} b$ .

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{a^{3} b + 3 a^{2} b x + 3 a b x^{2} + b x^{3}}{{(a + x)}^{3}}$

Langkah 5.2.4.4

Faktorkan $b$ dari $a^{3} b + 3 a^{2} b x + 3 a b x^{2} + b x^{3}$ .

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Langkah 5.2.4.4.1

Faktorkan $b$ dari $a^{3} b$ .

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b a^{3} + 3 a^{2} b x + 3 a b x^{2} + b x^{3}}{{(a + x)}^{3}}$

Langkah 5.2.4.4.2

Faktorkan $b$ dari $3 a^{2} b x$ .

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b a^{3} + b (3 a^{2} x) + 3 a b x^{2} + b x^{3}}{{(a + x)}^{3}}$

Langkah 5.2.4.4.3

Faktorkan $b$ dari $3 a b x^{2}$ .

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b a^{3} + b (3 a^{2} x) + b (3 a x^{2}) + b x^{3}}{{(a + x)}^{3}}$

Langkah 5.2.4.4.4

Faktorkan $b$ dari $b x^{3}$ .

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b a^{3} + b (3 a^{2} x) + b (3 a x^{2}) + b (x^{3})}{{(a + x)}^{3}}$

Langkah 5.2.4.4.5

Faktorkan $b$ dari $b a^{3} + b (3 a^{2} x)$ .

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b (a^{3} + 3 a^{2} x) + b (3 a x^{2}) + b (x^{3})}{{(a + x)}^{3}}$

Langkah 5.2.4.4.6

Faktorkan $b$ dari $b (a^{3} + 3 a^{2} x) + b (3 a x^{2})$ .

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b (a^{3} + 3 a^{2} x + 3 a x^{2}) + b (x^{3})}{{(a + x)}^{3}}$

Langkah 5.2.4.4.7

Faktorkan $b$ dari $b (a^{3} + 3 a^{2} x + 3 a x^{2}) + b (x^{3})$ .

$f^{- 1} (b {(x + a)}^{3} + c) = \frac{b (a^{3} + 3 a^{2} x + 3 a x^{2} + x^{3})}{{(a + x)}^{3}}$

Langkah 5.3

Evaluasi $f (f^{- 1} (b))$ .

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Langkah 5.3.1

Tulis fungsi hasil komposit.

$f (f^{- 1} (b))$

Langkah 5.3.2

Evaluasi $f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}})$ dengan mensubstitusikan nilai (Variabel1) ke dalam (Variabel2).

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) {(x + a)}^{3} + c$

Langkah 5.3.3

Sederhanakan setiap suku.

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Langkah 5.3.3.1

Gunakan Teorema Binomial.

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) (x^{3} + 3 x^{2} a + 3 x a^{2} + a^{3}) + c$

Langkah 5.3.3.2

Perluas $(\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) (x^{3} + 3 x^{2} a + 3 x a^{2} + a^{3})$ dengan mengalikan setiap suku dalam pernyataan pertama dengan setiap suku dalam pernyataan kedua.

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b}{{(x + a)}^{3}} \cdot x^{3} + \frac{b}{{(x + a)}^{3}} \cdot (3 x^{2} a) + \frac{b}{{(x + a)}^{3}} \cdot (3 x a^{2}) + \frac{b}{{(x + a)}^{3}} \cdot a^{3} - \frac{c}{{(x + a)}^{3}} \cdot x^{3} - \frac{c}{{(x + a)}^{3}} \cdot (3 x^{2} a) - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3

Sederhanakan setiap suku.

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Langkah 5.3.3.3.1

Gabungkan $\frac{b}{{(x + a)}^{3}}$ dan $x^{3}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{b}{{(x + a)}^{3}} \cdot (3 x^{2} a) + \frac{b}{{(x + a)}^{3}} \cdot (3 x a^{2}) + \frac{b}{{(x + a)}^{3}} \cdot a^{3} - \frac{c}{{(x + a)}^{3}} \cdot x^{3} - \frac{c}{{(x + a)}^{3}} \cdot (3 x^{2} a) - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.2

Tulis kembali menggunakan sifat komutatif dari perkalian.

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + 3 (\frac{b}{{(x + a)}^{3}}) \cdot (x^{2} a) + \frac{b}{{(x + a)}^{3}} \cdot (3 x a^{2}) + \frac{b}{{(x + a)}^{3}} \cdot a^{3} - \frac{c}{{(x + a)}^{3}} \cdot x^{3} - \frac{c}{{(x + a)}^{3}} \cdot (3 x^{2} a) - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.3

Gabungkan $3$ dan $\frac{b}{{(x + a)}^{3}}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 b}{{(x + a)}^{3}} \cdot (x^{2} a) + \frac{b}{{(x + a)}^{3}} \cdot (3 x a^{2}) + \frac{b}{{(x + a)}^{3}} \cdot a^{3} - \frac{c}{{(x + a)}^{3}} \cdot x^{3} - \frac{c}{{(x + a)}^{3}} \cdot (3 x^{2} a) - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.4

Kalikan $\frac{3 b}{{(x + a)}^{3}} (x^{2} a)$ .

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Langkah 5.3.3.3.4.1

Gabungkan $x^{2}$ dan $\frac{3 b}{{(x + a)}^{3}}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{x^{2} (3 b)}{{(x + a)}^{3}} \cdot a + \frac{b}{{(x + a)}^{3}} \cdot (3 x a^{2}) + \frac{b}{{(x + a)}^{3}} \cdot a^{3} - \frac{c}{{(x + a)}^{3}} \cdot x^{3} - \frac{c}{{(x + a)}^{3}} \cdot (3 x^{2} a) - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.4.2

Gabungkan $\frac{x^{2} (3 b)}{{(x + a)}^{3}}$ dan $a$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{x^{2} (3 b) a}{{(x + a)}^{3}} + \frac{b}{{(x + a)}^{3}} \cdot (3 x a^{2}) + \frac{b}{{(x + a)}^{3}} \cdot a^{3} - \frac{c}{{(x + a)}^{3}} \cdot x^{3} - \frac{c}{{(x + a)}^{3}} \cdot (3 x^{2} a) - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.5

Pindahkan $3$ ke sebelah kiri $x^{2}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 \cdot (x^{2} b a)}{{(x + a)}^{3}} + \frac{b}{{(x + a)}^{3}} \cdot (3 x a^{2}) + \frac{b}{{(x + a)}^{3}} \cdot a^{3} - \frac{c}{{(x + a)}^{3}} \cdot x^{3} - \frac{c}{{(x + a)}^{3}} \cdot (3 x^{2} a) - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.6

Tulis kembali menggunakan sifat komutatif dari perkalian.

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + 3 (\frac{b}{{(x + a)}^{3}}) \cdot (x a^{2}) + \frac{b}{{(x + a)}^{3}} \cdot a^{3} - \frac{c}{{(x + a)}^{3}} \cdot x^{3} - \frac{c}{{(x + a)}^{3}} \cdot (3 x^{2} a) - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.7

Gabungkan $3$ dan $\frac{b}{{(x + a)}^{3}}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 b}{{(x + a)}^{3}} \cdot (x a^{2}) + \frac{b}{{(x + a)}^{3}} \cdot a^{3} - \frac{c}{{(x + a)}^{3}} \cdot x^{3} - \frac{c}{{(x + a)}^{3}} \cdot (3 x^{2} a) - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.8

Kalikan $\frac{3 b}{{(x + a)}^{3}} (x a^{2})$ .

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Langkah 5.3.3.3.8.1

Gabungkan $x$ dan $\frac{3 b}{{(x + a)}^{3}}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{x (3 b)}{{(x + a)}^{3}} \cdot a^{2} + \frac{b}{{(x + a)}^{3}} \cdot a^{3} - \frac{c}{{(x + a)}^{3}} \cdot x^{3} - \frac{c}{{(x + a)}^{3}} \cdot (3 x^{2} a) - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.8.2

Gabungkan $\frac{x (3 b)}{{(x + a)}^{3}}$ dan $a^{2}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{x (3 b) a^{2}}{{(x + a)}^{3}} + \frac{b}{{(x + a)}^{3}} \cdot a^{3} - \frac{c}{{(x + a)}^{3}} \cdot x^{3} - \frac{c}{{(x + a)}^{3}} \cdot (3 x^{2} a) - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.9

Pindahkan $3$ ke sebelah kiri $x$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 \cdot (x b a^{2})}{{(x + a)}^{3}} + \frac{b}{{(x + a)}^{3}} \cdot a^{3} - \frac{c}{{(x + a)}^{3}} \cdot x^{3} - \frac{c}{{(x + a)}^{3}} \cdot (3 x^{2} a) - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.10

Gabungkan $\frac{b}{{(x + a)}^{3}}$ dan $a^{3}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}} \cdot x^{3} - \frac{c}{{(x + a)}^{3}} \cdot (3 x^{2} a) - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.11

Gabungkan $x^{3}$ dan $\frac{c}{{(x + a)}^{3}}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}} \cdot (3 x^{2} a) - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.12

Kalikan $- \frac{c}{{(x + a)}^{3}} (3 x^{2} a)$ .

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Langkah 5.3.3.3.12.1

Kalikan $3$ dengan $- 1$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - 3 \frac{c}{{(x + a)}^{3}} \cdot (x^{2} a) - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.12.2

Gabungkan $- 3$ dan $\frac{c}{{(x + a)}^{3}}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} + \frac{- 3 c}{{(x + a)}^{3}} \cdot (x^{2} a) - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.12.3

Gabungkan $x^{2}$ dan $\frac{- 3 c}{{(x + a)}^{3}}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} + \frac{x^{2} (- 3 c)}{{(x + a)}^{3}} \cdot a - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.12.4

Gabungkan $\frac{x^{2} (- 3 c)}{{(x + a)}^{3}}$ dan $a$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} + \frac{x^{2} (- 3 c) a}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.13

Hilangkan tanda kurung yang tidak perlu.

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} + \frac{x^{2} \cdot (- 3 c a)}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.14

Pindahkan $- 3$ ke sebelah kiri $x^{2}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} + \frac{- 3 \cdot (x^{2} c a)}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.15

Pindahkan tanda negatif di depan pecahan.

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{(3) \cdot (x^{2} c a)}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}} \cdot (3 x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.16

Kalikan $- \frac{c}{{(x + a)}^{3}} (3 x a^{2})$ .

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Langkah 5.3.3.3.16.1

Kalikan $3$ dengan $- 1$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} - 3 \frac{c}{{(x + a)}^{3}} \cdot (x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.16.2

Gabungkan $- 3$ dan $\frac{c}{{(x + a)}^{3}}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} + \frac{- 3 c}{{(x + a)}^{3}} \cdot (x a^{2}) - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.16.3

Gabungkan $x$ dan $\frac{- 3 c}{{(x + a)}^{3}}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} + \frac{x (- 3 c)}{{(x + a)}^{3}} \cdot a^{2} - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.16.4

Gabungkan $\frac{x (- 3 c)}{{(x + a)}^{3}}$ dan $a^{2}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} + \frac{x (- 3 c) a^{2}}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.17

Hilangkan tanda kurung yang tidak perlu.

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} + \frac{x \cdot (- 3 c a^{2})}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.18

Pindahkan $- 3$ ke sebelah kiri $x$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} + \frac{- 3 \cdot (x c a^{2})}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.19

Pindahkan tanda negatif di depan pecahan.

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} - \frac{(3) \cdot (x c a^{2})}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}} \cdot a^{3} + c$

Langkah 5.3.3.3.20

Gabungkan $a^{3}$ dan $\frac{c}{{(x + a)}^{3}}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(x + a)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} - \frac{3 x c a^{2}}{{(x + a)}^{3}} - \frac{a^{3} c}{{(x + a)}^{3}} + c$

Langkah 5.3.4

Sederhanakan pernyataannya.

Ketuk untuk lebih banyak langkah...

Langkah 5.3.4.1

Susun kembali $x$ dan $a$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(a + x)}^{3}} + \frac{3 x^{2} b a}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} - \frac{3 x c a^{2}}{{(x + a)}^{3}} - \frac{a^{3} c}{{(x + a)}^{3}} + c$

Langkah 5.3.4.2

Pindahkan $x^{2}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(a + x)}^{3}} + \frac{3 b a x^{2}}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} - \frac{3 x c a^{2}}{{(x + a)}^{3}} - \frac{a^{3} c}{{(x + a)}^{3}} + c$

Langkah 5.3.4.3

Pindahkan $b$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(a + x)}^{3}} + \frac{3 a b x^{2}}{{(x + a)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} - \frac{3 x c a^{2}}{{(x + a)}^{3}} - \frac{a^{3} c}{{(x + a)}^{3}} + c$

Langkah 5.3.4.4

Susun kembali $x$ dan $a$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(a + x)}^{3}} + \frac{3 a b x^{2}}{{(a + x)}^{3}} + \frac{3 x b a^{2}}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} - \frac{3 x c a^{2}}{{(x + a)}^{3}} - \frac{a^{3} c}{{(x + a)}^{3}} + c$

Langkah 5.3.4.5

Pindahkan $x$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(a + x)}^{3}} + \frac{3 a b x^{2}}{{(a + x)}^{3}} + \frac{3 b a^{2} x}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} - \frac{3 x c a^{2}}{{(x + a)}^{3}} - \frac{a^{3} c}{{(x + a)}^{3}} + c$

Langkah 5.3.4.6

Pindahkan $b$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(a + x)}^{3}} + \frac{3 a b x^{2}}{{(a + x)}^{3}} + \frac{3 a^{2} b x}{{(x + a)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} - \frac{3 x c a^{2}}{{(x + a)}^{3}} - \frac{a^{3} c}{{(x + a)}^{3}} + c$

Langkah 5.3.4.7

Susun kembali $x$ dan $a$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(a + x)}^{3}} + \frac{3 a b x^{2}}{{(a + x)}^{3}} + \frac{3 a^{2} b x}{{(a + x)}^{3}} + \frac{b a^{3}}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} - \frac{3 x c a^{2}}{{(x + a)}^{3}} - \frac{a^{3} c}{{(x + a)}^{3}} + c$

Langkah 5.3.4.8

Susun kembali $b$ dan $a^{3}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(a + x)}^{3}} + \frac{3 a b x^{2}}{{(a + x)}^{3}} + \frac{3 a^{2} b x}{{(a + x)}^{3}} + \frac{a^{3} b}{{(x + a)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} - \frac{3 x c a^{2}}{{(x + a)}^{3}} - \frac{a^{3} c}{{(x + a)}^{3}} + c$

Langkah 5.3.4.9

Susun kembali $x$ dan $a$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(a + x)}^{3}} + \frac{3 a b x^{2}}{{(a + x)}^{3}} + \frac{3 a^{2} b x}{{(a + x)}^{3}} + \frac{a^{3} b}{{(a + x)}^{3}} - \frac{x^{3} c}{{(x + a)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} - \frac{3 x c a^{2}}{{(x + a)}^{3}} - \frac{a^{3} c}{{(x + a)}^{3}} + c$

Langkah 5.3.4.10

Susun kembali $x^{3}$ dan $c$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(a + x)}^{3}} + \frac{3 a b x^{2}}{{(a + x)}^{3}} + \frac{3 a^{2} b x}{{(a + x)}^{3}} + \frac{a^{3} b}{{(a + x)}^{3}} - \frac{c x^{3}}{{(x + a)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} - \frac{3 x c a^{2}}{{(x + a)}^{3}} - \frac{a^{3} c}{{(x + a)}^{3}} + c$

Langkah 5.3.4.11

Susun kembali $x$ dan $a$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(a + x)}^{3}} + \frac{3 a b x^{2}}{{(a + x)}^{3}} + \frac{3 a^{2} b x}{{(a + x)}^{3}} + \frac{a^{3} b}{{(a + x)}^{3}} - \frac{c x^{3}}{{(a + x)}^{3}} - \frac{3 x^{2} c a}{{(x + a)}^{3}} - \frac{3 x c a^{2}}{{(x + a)}^{3}} - \frac{a^{3} c}{{(x + a)}^{3}} + c$

Langkah 5.3.4.12

Pindahkan $x^{2}$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(a + x)}^{3}} + \frac{3 a b x^{2}}{{(a + x)}^{3}} + \frac{3 a^{2} b x}{{(a + x)}^{3}} + \frac{a^{3} b}{{(a + x)}^{3}} - \frac{c x^{3}}{{(a + x)}^{3}} - \frac{3 c a x^{2}}{{(x + a)}^{3}} - \frac{3 x c a^{2}}{{(x + a)}^{3}} - \frac{a^{3} c}{{(x + a)}^{3}} + c$

Langkah 5.3.4.13

Pindahkan $c$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(a + x)}^{3}} + \frac{3 a b x^{2}}{{(a + x)}^{3}} + \frac{3 a^{2} b x}{{(a + x)}^{3}} + \frac{a^{3} b}{{(a + x)}^{3}} - \frac{c x^{3}}{{(a + x)}^{3}} - \frac{3 a c x^{2}}{{(x + a)}^{3}} - \frac{3 x c a^{2}}{{(x + a)}^{3}} - \frac{a^{3} c}{{(x + a)}^{3}} + c$

Langkah 5.3.4.14

Susun kembali $x$ dan $a$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(a + x)}^{3}} + \frac{3 a b x^{2}}{{(a + x)}^{3}} + \frac{3 a^{2} b x}{{(a + x)}^{3}} + \frac{a^{3} b}{{(a + x)}^{3}} - \frac{c x^{3}}{{(a + x)}^{3}} - \frac{3 a c x^{2}}{{(a + x)}^{3}} - \frac{3 x c a^{2}}{{(x + a)}^{3}} - \frac{a^{3} c}{{(x + a)}^{3}} + c$

Langkah 5.3.4.15

Pindahkan $x$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(a + x)}^{3}} + \frac{3 a b x^{2}}{{(a + x)}^{3}} + \frac{3 a^{2} b x}{{(a + x)}^{3}} + \frac{a^{3} b}{{(a + x)}^{3}} - \frac{c x^{3}}{{(a + x)}^{3}} - \frac{3 a c x^{2}}{{(a + x)}^{3}} - \frac{3 c a^{2} x}{{(x + a)}^{3}} - \frac{a^{3} c}{{(x + a)}^{3}} + c$

Langkah 5.3.4.16

Pindahkan $c$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(a + x)}^{3}} + \frac{3 a b x^{2}}{{(a + x)}^{3}} + \frac{3 a^{2} b x}{{(a + x)}^{3}} + \frac{a^{3} b}{{(a + x)}^{3}} - \frac{c x^{3}}{{(a + x)}^{3}} - \frac{3 a c x^{2}}{{(a + x)}^{3}} - \frac{3 a^{2} c x}{{(x + a)}^{3}} - \frac{a^{3} c}{{(x + a)}^{3}} + c$

Langkah 5.3.4.17

Susun kembali $x$ dan $a$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(a + x)}^{3}} + \frac{3 a b x^{2}}{{(a + x)}^{3}} + \frac{3 a^{2} b x}{{(a + x)}^{3}} + \frac{a^{3} b}{{(a + x)}^{3}} - \frac{c x^{3}}{{(a + x)}^{3}} - \frac{3 a c x^{2}}{{(a + x)}^{3}} - \frac{3 a^{2} c x}{{(a + x)}^{3}} - \frac{a^{3} c}{{(x + a)}^{3}} + c$

Langkah 5.3.4.18

Susun kembali $x$ dan $a$ .

$f (\frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}) = \frac{b x^{3}}{{(a + x)}^{3}} + \frac{3 a b x^{2}}{{(a + x)}^{3}} + \frac{3 a^{2} b x}{{(a + x)}^{3}} + \frac{a^{3} b}{{(a + x)}^{3}} - \frac{c x^{3}}{{(a + x)}^{3}} - \frac{3 a c x^{2}}{{(a + x)}^{3}} - \frac{3 a^{2} c x}{{(a + x)}^{3}} - \frac{a^{3} c}{{(a + x)}^{3}} + c$

Langkah 5.4

Karena $f^{- 1} (f (b)) = b$ dan $f (f^{- 1} (b)) = b$ , maka $f^{- 1} (b) = \frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}$ merupakan balikan dari $f (b) = b {(x + a)}^{3} + c$ .

$f^{- 1} (b) = \frac{b}{{(x + a)}^{3}} - \frac{c}{{(x + a)}^{3}}$