Basic Math Examples

$\frac{\frac{\frac{8 m - 16}{3 m + 3}}{5 m - 10}}{2 m + 2}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{\frac{8 m - 16}{3 m + 3}}{5 m - 10} \cdot \frac{1}{2 m + 2}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{8 m - 16}{3 m + 3} \cdot \frac{1}{5 m - 10} \frac{1}{2 m + 2}$

Step 3

Factor $8$ out of $8 m - 16$ .

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Step 3.1

Factor $8$ out of $8 m$ .

$\frac{8 (m) - 16}{3 m + 3} \cdot \frac{1}{5 m - 10} \frac{1}{2 m + 2}$

Step 3.2

Factor $8$ out of $- 16$ .

$\frac{8 m + 8 \cdot - 2}{3 m + 3} \cdot \frac{1}{5 m - 10} \frac{1}{2 m + 2}$

Step 3.3

Factor $8$ out of $8 m + 8 \cdot - 2$ .

$\frac{8 (m - 2)}{3 m + 3} \cdot \frac{1}{5 m - 10} \frac{1}{2 m + 2}$

Step 4

Factor $3$ out of $3 m + 3$ .

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Step 4.1

Factor $3$ out of $3 m$ .

$\frac{8 (m - 2)}{3 (m) + 3} \cdot \frac{1}{5 m - 10} \frac{1}{2 m + 2}$

Step 4.2

Factor $3$ out of $3$ .

$\frac{8 (m - 2)}{3 (m) + 3 (1)} \cdot \frac{1}{5 m - 10} \frac{1}{2 m + 2}$

Step 4.3

Factor $3$ out of $3 (m) + 3 (1)$ .

$\frac{8 (m - 2)}{3 (m + 1)} \cdot \frac{1}{5 m - 10} \frac{1}{2 m + 2}$

Step 5

Factor $5$ out of $5 m - 10$ .

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Step 5.1

Factor $5$ out of $5 m$ .

$\frac{8 (m - 2)}{3 (m + 1)} \cdot \frac{1}{5 (m) - 10} \frac{1}{2 m + 2}$

Step 5.2

Factor $5$ out of $- 10$ .

$\frac{8 (m - 2)}{3 (m + 1)} \cdot \frac{1}{5 m + 5 \cdot - 2} \frac{1}{2 m + 2}$

Step 5.3

Factor $5$ out of $5 m + 5 \cdot - 2$ .

$\frac{8 (m - 2)}{3 (m + 1)} \cdot \frac{1}{5 (m - 2)} \frac{1}{2 m + 2}$

Step 6

Cancel the common factor of $m - 2$ .

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Step 6.1

Factor $m - 2$ out of $8 (m - 2)$ .

$\frac{(m - 2) \cdot 8}{3 (m + 1)} \cdot \frac{1}{5 (m - 2)} \frac{1}{2 m + 2}$

Step 6.2

Factor $m - 2$ out of $5 (m - 2)$ .

$\frac{(m - 2) \cdot 8}{3 (m + 1)} \cdot \frac{1}{(m - 2) \cdot 5} \frac{1}{2 m + 2}$

Step 6.3

Cancel the common factor.

$\frac{(m - 2) \cdot 8}{3 (m + 1)} \cdot \frac{1}{(m - 2) \cdot 5} \frac{1}{2 m + 2}$

Step 6.4

Rewrite the expression.

$\frac{8}{3 (m + 1)} \cdot \frac{1}{5} \frac{1}{2 m + 2}$

Step 7

Multiply $\frac{8}{3 (m + 1)}$ by $\frac{1}{5}$ .

$\frac{8}{3 (m + 1) \cdot 5} \cdot \frac{1}{2 m + 2}$

Step 8

Multiply $5$ by $3$ .

$\frac{8}{15 (m + 1)} \cdot \frac{1}{2 m + 2}$

Step 9

Factor $2$ out of $2 m + 2$ .

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Step 9.1

Factor $2$ out of $2 m$ .

$\frac{8}{15 (m + 1)} \cdot \frac{1}{2 (m) + 2}$

Step 9.2

Factor $2$ out of $2$ .

$\frac{8}{15 (m + 1)} \cdot \frac{1}{2 (m) + 2 (1)}$

Step 9.3

Factor $2$ out of $2 (m) + 2 (1)$ .

$\frac{8}{15 (m + 1)} \cdot \frac{1}{2 (m + 1)}$

Step 10

Cancel the common factor of $2$ .

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Step 10.1

Factor $2$ out of $8$ .

$\frac{2 (4)}{15 (m + 1)} \cdot \frac{1}{2 (m + 1)}$

Step 10.2

Cancel the common factor.

$\frac{2 \cdot 4}{15 (m + 1)} \cdot \frac{1}{2 (m + 1)}$

Step 10.3

Rewrite the expression.

$\frac{4}{15 (m + 1)} \cdot \frac{1}{m + 1}$

Step 11

Multiply $\frac{4}{15 (m + 1)}$ by $\frac{1}{m + 1}$ .

$\frac{4}{15 (m + 1) (m + 1)}$

Step 12

Raise $m + 1$ to the power of $1$ .

$\frac{4}{15 ({(m + 1)}^{1} (m + 1))}$

Step 13

Raise $m + 1$ to the power of $1$ .

$\frac{4}{15 ({(m + 1)}^{1} {(m + 1)}^{1})}$

Step 14

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

$\frac{4}{15 {(m + 1)}^{1 + 1}}$

Step 15

Add $1$ and $1$ .

$\frac{4}{15 {(m + 1)}^{2}}$