Algebra Examples

$\frac{\frac{\frac{n - 15}{9 n}}{15 - n}}{3 n^{5}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{\frac{n - 15}{9 n}}{15 - n} \cdot \frac{1}{3 n^{5}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{n - 15}{9 n} \cdot \frac{1}{15 - n} \frac{1}{3 n^{5}}$

Step 3

Multiply $\frac{n - 15}{9 n}$ by $\frac{1}{15 - n}$ .

$\frac{n - 15}{9 n (15 - n)} \cdot \frac{1}{3 n^{5}}$

Step 4

Cancel the common factor of $n - 15$ and $15 - n$ .

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Step 4.1

Factor $- 1$ out of $n$ .

$\frac{- 1 (- n) - 15}{9 n (15 - n)} \cdot \frac{1}{3 n^{5}}$

Step 4.2

Rewrite $- 15$ as $- 1 (15)$ .

$\frac{- 1 (- n) - 1 (15)}{9 n (15 - n)} \cdot \frac{1}{3 n^{5}}$

Step 4.3

Factor $- 1$ out of $- 1 (- n) - 1 (15)$ .

$\frac{- 1 (- n + 15)}{9 n (15 - n)} \cdot \frac{1}{3 n^{5}}$

Step 4.4

Reorder terms.

$\frac{- 1 (- n + 15)}{9 n (- n + 15)} \cdot \frac{1}{3 n^{5}}$

Step 4.5

Cancel the common factor.

$\frac{- 1 (- n + 15)}{9 n (- n + 15)} \cdot \frac{1}{3 n^{5}}$

Step 4.6

Rewrite the expression.

$\frac{- 1}{9 n} \cdot \frac{1}{3 n^{5}}$

Step 5

Combine.

$\frac{- 1 \cdot 1}{9 n (3 n^{5})}$

Step 6

Multiply $n$ by $n^{5}$ by adding the exponents.

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Step 6.1

Move $n^{5}$ .

$\frac{- 1 \cdot 1}{9 (n^{5} n) \cdot 3}$

Step 6.2

Multiply $n^{5}$ by $n$ .

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Step 6.2.1

Raise $n$ to the power of $1$ .

$\frac{- 1 \cdot 1}{9 (n^{5} n^{1}) \cdot 3}$

Step 6.2.2

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

$\frac{- 1 \cdot 1}{9 n^{5 + 1} \cdot 3}$

Step 6.3

Add $5$ and $1$ .

$\frac{- 1 \cdot 1}{9 n^{6} \cdot 3}$

Step 7

Multiply $- 1$ by $1$ .

$\frac{- 1}{9 n^{6} \cdot 3}$

Step 8

Multiply $3$ by $9$ .

$\frac{- 1}{27 n^{6}}$

Step 9

Move the negative in front of the fraction.

$- \frac{1}{27 n^{6}}$