Algebra Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Cancel the common factor of $3 n$ .

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Step 2.1

Factor $3 n$ out of $9 n$ .

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

Step 2.2

Factor $3 n$ out of $3 n^{5}$ .

$\frac{n - 15}{3 n (3)} \cdot \frac{3 n (n^{4})}{15 - n}$

Step 2.3

Cancel the common factor.

$\frac{n - 15}{3 n \cdot 3} \cdot \frac{3 n \cdot n^{4}}{15 - n}$

Step 2.4

Rewrite the expression.

$\frac{n - 15}{3} \cdot \frac{n^{4}}{15 - n}$

Step 3

Multiply $\frac{n - 15}{3}$ by $\frac{n^{4}}{15 - n}$ .

$\frac{(n - 15) n^{4}}{3 (15 - n)}$

Step 4

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

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Step 4.1

Factor $- 1$ out of $n$ .

$\frac{(- 1 (- n) - 15) n^{4}}{3 (15 - n)}$

Step 4.2

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

$\frac{(- 1 (- n) - 1 (15)) n^{4}}{3 (15 - n)}$

Step 4.3

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

$\frac{- 1 (- n + 15) n^{4}}{3 (15 - n)}$

Step 4.4

Reorder terms.

$\frac{- 1 (- n + 15) n^{4}}{3 (- n + 15)}$

Step 4.5

Cancel the common factor.

$\frac{- 1 (- n + 15) n^{4}}{3 (- n + 15)}$

Step 4.6

Rewrite the expression.

$\frac{- 1 n^{4}}{3}$

Step 5

Move the negative in front of the fraction.

$- \frac{n^{4}}{3}$