Pre-Algebra Examples

$g (x) = \frac{x + 1}{x^{2} - 1}$

Step 1

Rewrite the function as an equation.

$y = \frac{x + 1}{x^{2} - 1}$

Step 2

Simplify $\frac{x + 1}{x^{2} - 1}$ .

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Step 2.1

Simplify the denominator.

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Step 2.1.1

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

$y = \frac{x + 1}{x^{2} - 1^{2}}$

Step 2.1.2

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 $b = 1$ .

$y = \frac{x + 1}{(x + 1) (x - 1)}$

Step 2.2

Cancel the common factor of $x + 1$ .

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Step 2.2.1

Cancel the common factor.

$y = \frac{x + 1}{(x + 1) (x - 1)}$

Step 2.2.2

Rewrite the expression.

$y = \frac{1}{x - 1}$