Algebra Examples

$\frac{x^{2} - 4}{x^{2} + 5 x + 6}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{x^{2} - 2^{2}}{x^{2} + 5 x + 6}$

Step 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 $b = 2$ .

$\frac{(x + 2) (x - 2)}{x^{2} + 5 x + 6}$

Step 2

Factor $x^{2} + 5 x + 6$ using the AC method.

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Step 2.1

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 $6$ and whose sum is $5$ .

$2, 3$

Step 2.2

Write the factored form using these integers.

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

Step 3

Cancel the common factor of $x + 2$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{x - 2}{x + 3}$