Basic Math Examples

$\frac{7 n^{3} + 70 n^{3}}{10 - n} \div \frac{n + 15}{n - 10}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{7 n^{3} + 70 n^{3}}{10 - n} \cdot \frac{n - 10}{n + 15}$

Step 2

Add $7 n^{3}$ and $70 n^{3}$ .

$\frac{77 n^{3}}{10 - n} \cdot \frac{n - 10}{n + 15}$

Step 3

Multiply $\frac{77 n^{3}}{10 - n}$ by $\frac{n - 10}{n + 15}$ .

$\frac{77 n^{3} (n - 10)}{(10 - n) (n + 15)}$

Step 4

Cancel the common factor of $n - 10$ and $10 - n$ .

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Step 4.1

Factor $- 1$ out of $n$ .

$\frac{77 n^{3} (- 1 (- n) - 10)}{(10 - n) (n + 15)}$

Step 4.2

Rewrite $- 10$ as $- 1 (10)$ .

$\frac{77 n^{3} (- 1 (- n) - 1 (10))}{(10 - n) (n + 15)}$

Step 4.3

Factor $- 1$ out of $- 1 (- n) - 1 (10)$ .

$\frac{77 n^{3} (- 1 (- n + 10))}{(10 - n) (n + 15)}$

Step 4.4

Reorder terms.

$\frac{77 n^{3} (- 1 (- n + 10))}{(- n + 10) (n + 15)}$

Step 4.5

Cancel the common factor.

$\frac{77 n^{3} (- 1 (- n + 10))}{(- n + 10) (n + 15)}$

Step 4.6

Rewrite the expression.

$\frac{77 n^{3} \cdot (- 1)}{n + 15}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $- 1$ by $77$ .

$\frac{- 77 n^{3}}{n + 15}$

Step 5.2

Move the negative in front of the fraction.

$- \frac{77 n^{3}}{n + 15}$