Simplify (x^2+7x+12)/(x^2-x-12)

$\frac{x^{2} + 7 x + 12}{x^{2} - x - 12}$

Step 1

Factor $x^{2} + 7 x + 12$ 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 $12$ and whose sum is $7$ .

$3, 4$

Write the factored form using these integers.

$\frac{(x + 3) (x + 4)}{x^{2} - x - 12}$

Step 2

Factor $x^{2} - x - 12$ 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 $- 12$ and whose sum is $- 1$ .

$- 4, 3$

Write the factored form using these integers.

$\frac{(x + 3) (x + 4)}{(x - 4) (x + 3)}$

Step 3

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{(x + 3) (x + 4)}{(x - 4) (x + 3)}$

Rewrite the expression.

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

Simplify (x^2+7x+12)/(x^2-x-12)

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