Simplify (2b-2)/(2b^2-8)

$\frac{2 b - 2}{2 b^{2} - 8}$

Step 1

Cancel the common factor of $2 b - 2$ and $2 b^{2} - 8$ .

Factor $2$ out of $2 b$ .

$\frac{2 (b) - 2}{2 b^{2} - 8}$

Factor $2$ out of $- 2$ .

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

Factor $2$ out of $2 (b) + 2 (- 1)$ .

$\frac{2 (b - 1)}{2 b^{2} - 8}$

Cancel the common factors.

Factor $2$ out of $2 b^{2}$ .

$\frac{2 (b - 1)}{2 (b^{2}) - 8}$

Factor $2$ out of $- 8$ .

$\frac{2 (b - 1)}{2 b^{2} + 2 \cdot - 4}$

Factor $2$ out of $2 b^{2} + 2 \cdot - 4$ .

$\frac{2 (b - 1)}{2 (b^{2} - 4)}$

Cancel the common factor.

$\frac{2 (b - 1)}{2 (b^{2} - 4)}$

Rewrite the expression.

$\frac{b - 1}{b^{2} - 4}$

Step 2

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

$\frac{b - 1}{b^{2} - 2^{2}}$

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

$\frac{b - 1}{(b + 2) (b - 2)}$