Simplify (x^2+5x-36)/(x^2-16)

$\frac{x^{2} + 5 x - 36}{x^{2} - 16}$

Step 1

Factor $x^{2} + 5 x - 36$ using the AC method.

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 $- 36$ and whose sum is $5$ .

$- 4, 9$

Write the factored form using these integers.

$\frac{(x - 4) (x + 9)}{x^{2} - 16}$

Step 2

Simplify the denominator.

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

$\frac{(x - 4) (x + 9)}{x^{2} - 4^{2}}$

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 $b = 4$ .

$\frac{(x - 4) (x + 9)}{(x + 4) (x - 4)}$

Step 3

Cancel the common factor of $x - 4$ .

Cancel the common factor.

$\frac{(x - 4) (x + 9)}{(x + 4) (x - 4)}$

Rewrite the expression.

$\frac{x + 9}{x + 4}$

Simplify (x^2+5x-36)/(x^2-16)

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