Algebra Examples

$\frac{a^{2} - b^{2}}{2 a - 2 b} \div \frac{8}{a + b}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{a^{2} - b^{2}}{2 a - 2 b} \cdot \frac{a + b}{8}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = b$ .

$\frac{(a + b) (a - b)}{2 a - 2 b} \cdot \frac{a + b}{8}$

Step 3

Simplify terms.

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Step 3.1

Factor $2$ out of $2 a - 2 b$ .

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Step 3.1.1

Factor $2$ out of $2 a$ .

$\frac{(a + b) (a - b)}{2 (a) - 2 b} \cdot \frac{a + b}{8}$

Step 3.1.2

Factor $2$ out of $- 2 b$ .

$\frac{(a + b) (a - b)}{2 (a) + 2 (- b)} \cdot \frac{a + b}{8}$

Step 3.1.3

Factor $2$ out of $2 (a) + 2 (- b)$ .

$\frac{(a + b) (a - b)}{2 (a - b)} \cdot \frac{a + b}{8}$

Step 3.2

Cancel the common factor of $a - b$ .

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Step 3.2.1

Cancel the common factor.

$\frac{(a + b) (a - b)}{2 (a - b)} \cdot \frac{a + b}{8}$

Step 3.2.2

Rewrite the expression.

$\frac{a + b}{2} \cdot \frac{a + b}{8}$

Step 4

Multiply $\frac{a + b}{2} \cdot \frac{a + b}{8}$ .

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Step 4.1

Multiply $\frac{a + b}{2}$ by $\frac{a + b}{8}$ .

$\frac{(a + b) (a + b)}{2 \cdot 8}$

Step 4.2

Raise $a + b$ to the power of $1$ .

$\frac{{(a + b)}^{1} (a + b)}{2 \cdot 8}$

Step 4.3

Raise $a + b$ to the power of $1$ .

$\frac{{(a + b)}^{1} {(a + b)}^{1}}{2 \cdot 8}$

Step 4.4

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

$\frac{{(a + b)}^{1 + 1}}{2 \cdot 8}$

Step 4.5

Add $1$ and $1$ .

$\frac{{(a + b)}^{2}}{2 \cdot 8}$

Step 4.6

Multiply $2$ by $8$ .

$\frac{{(a + b)}^{2}}{16}$