Algebra Examples

$\frac{2 x - 2}{3} \cdot \frac{2}{x^{2} - 1}$

Step 1

Factor $2$ out of $2 x - 2$ .

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Step 1.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) - 2}{3} \cdot \frac{2}{x^{2} - 1}$

Step 1.2

Factor $2$ out of $- 2$ .

$\frac{2 (x) + 2 (- 1)}{3} \cdot \frac{2}{x^{2} - 1}$

Step 1.3

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

$\frac{2 (x - 1)}{3} \cdot \frac{2}{x^{2} - 1}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

$\frac{2 (x - 1)}{3} \cdot \frac{2}{x^{2} - 1^{2}}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$\frac{2 (x - 1)}{3} \cdot \frac{2}{(x + 1) (x - 1)}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $x - 1$ .

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Step 3.1.1

Factor $x - 1$ out of $2 (x - 1)$ .

$\frac{(x - 1) \cdot 2}{3} \cdot \frac{2}{(x + 1) (x - 1)}$

Step 3.1.2

Factor $x - 1$ out of $(x + 1) (x - 1)$ .

$\frac{(x - 1) \cdot 2}{3} \cdot \frac{2}{(x - 1) (x + 1)}$

Step 3.1.3

Cancel the common factor.

$\frac{(x - 1) \cdot 2}{3} \cdot \frac{2}{(x - 1) (x + 1)}$

Step 3.1.4

Rewrite the expression.

$\frac{2}{3} \cdot \frac{2}{x + 1}$

Step 3.2

Multiply $\frac{2}{3}$ by $\frac{2}{x + 1}$ .

$\frac{2 \cdot 2}{3 (x + 1)}$

Step 3.3

Multiply $2$ by $2$ .

$\frac{4}{3 (x + 1)}$