Simplify (x^2-x-2)/(x^2-1)

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

Factor $x^{2} - x - 2$ using the AC method.

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Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 2$ and whose sum is $- 1$ .

$- 2, 1$

Write the factored form using these integers.

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

Simplify the denominator.

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

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

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 $b = 1$ .

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

Cancel the common factor of $x + 1$ .

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Cancel the common factor.

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

Rewrite the expression.

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

Simplify (x^2-x-2)/(x^2-1)

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