Algebra Examples

$\frac{2 a + 2}{a^{2} - 1}$

Step 1

Factor $2$ out of $2 a + 2$ .

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Step 1.1

Factor $2$ out of $2 a$ .

$\frac{2 (a) + 2}{a^{2} - 1}$

Step 1.2

Factor $2$ out of $2$ .

$\frac{2 (a) + 2 (1)}{a^{2} - 1}$

Step 1.3

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

$\frac{2 (a + 1)}{a^{2} - 1}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{2 (a + 1)}{a^{2} - 1^{2}}$

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 $a = a$ and $b = 1$ .

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

Step 3

Cancel the common factor of $a + 1$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{2}{a - 1}$