Algebra Examples

$\frac{x^{2} + 2 x - 8}{x^{2} - 16}$

Step 1

Factor $x^{2} + 2 x - 8$ using the AC method.

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Step 1.1

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 $- 8$ and whose sum is $2$ .

$- 2, 4$

Step 1.2

Write the factored form using these integers.

$\frac{(x - 2) (x + 4)}{x^{2} - 16}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $16$ as $4^{2}$ .

$\frac{(x - 2) (x + 4)}{x^{2} - 4^{2}}$

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 $b = 4$ .

$\frac{(x - 2) (x + 4)}{(x + 4) (x - 4)}$

Step 3

Cancel the common factor of $x + 4$ .

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Step 3.1

Cancel the common factor.

$\frac{(x - 2) (x + 4)}{(x + 4) (x - 4)}$

Step 3.2

Rewrite the expression.

$\frac{x - 2}{x - 4}$