Algebra Examples

$f (x) = 4 {(x + 1)}^{\frac{2}{3}} + \frac{28 x}{{(x + 1)}^{\frac{1}{3}}}$

Step 1

Write $f (x) = 4 {(x + 1)}^{\frac{2}{3}} + \frac{28 x}{{(x + 1)}^{\frac{1}{3}}}$ as an equation.

$y = 4 {(x + 1)}^{\frac{2}{3}} + \frac{28 x}{{(x + 1)}^{\frac{1}{3}}}$

Step 2

Simplify $4 {(x + 1)}^{\frac{2}{3}} + \frac{28 x}{{(x + 1)}^{\frac{1}{3}}}$ .

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Step 2.1

To write $4 {(x + 1)}^{\frac{2}{3}}$ as a fraction with a common denominator, multiply by $\frac{{(x + 1)}^{\frac{1}{3}}}{{(x + 1)}^{\frac{1}{3}}}$ .

$y = \frac{4 {(x + 1)}^{\frac{2}{3}} {(x + 1)}^{\frac{1}{3}}}{{(x + 1)}^{\frac{1}{3}}} + \frac{28 x}{{(x + 1)}^{\frac{1}{3}}}$

Step 2.2

Combine the numerators over the common denominator.

$y = \frac{4 {(x + 1)}^{\frac{2}{3}} {(x + 1)}^{\frac{1}{3}} + 28 x}{{(x + 1)}^{\frac{1}{3}}}$

Step 2.3

Simplify the numerator.

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Step 2.3.1

Factor $4$ out of $4 {(x + 1)}^{\frac{2}{3}} {(x + 1)}^{\frac{1}{3}} + 28 x$ .

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Step 2.3.1.1

Factor $4$ out of $4 {(x + 1)}^{\frac{2}{3}} {(x + 1)}^{\frac{1}{3}}$ .

$y = \frac{4 ({(x + 1)}^{\frac{2}{3}} {(x + 1)}^{\frac{1}{3}}) + 28 x}{{(x + 1)}^{\frac{1}{3}}}$

Step 2.3.1.2

Factor $4$ out of $28 x$ .

$y = \frac{4 ({(x + 1)}^{\frac{2}{3}} {(x + 1)}^{\frac{1}{3}}) + 4 (7 x)}{{(x + 1)}^{\frac{1}{3}}}$

Step 2.3.1.3

Factor $4$ out of $4 ({(x + 1)}^{\frac{2}{3}} {(x + 1)}^{\frac{1}{3}}) + 4 (7 x)$ .

$y = \frac{4 ({(x + 1)}^{\frac{2}{3}} {(x + 1)}^{\frac{1}{3}} + 7 x)}{{(x + 1)}^{\frac{1}{3}}}$

Step 2.3.2

Multiply ${(x + 1)}^{\frac{2}{3}}$ by ${(x + 1)}^{\frac{1}{3}}$ by adding the exponents.

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Step 2.3.2.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = \frac{4 ({(x + 1)}^{\frac{2}{3} + \frac{1}{3}} + 7 x)}{{(x + 1)}^{\frac{1}{3}}}$

Step 2.3.2.2

Combine the numerators over the common denominator.

$y = \frac{4 ({(x + 1)}^{\frac{2 + 1}{3}} + 7 x)}{{(x + 1)}^{\frac{1}{3}}}$

Step 2.3.2.3

Add $2$ and $1$ .

$y = \frac{4 ({(x + 1)}^{\frac{3}{3}} + 7 x)}{{(x + 1)}^{\frac{1}{3}}}$

Step 2.3.2.4

Divide $3$ by $3$ .

$y = \frac{4 ({(x + 1)}^{1} + 7 x)}{{(x + 1)}^{\frac{1}{3}}}$

Step 2.3.3

Simplify ${(x + 1)}^{1}$ .

$y = \frac{4 (x + 1 + 7 x)}{{(x + 1)}^{\frac{1}{3}}}$

Step 2.3.4

Add $x$ and $7 x$ .

$y = \frac{4 (8 x + 1)}{{(x + 1)}^{\frac{1}{3}}}$