Simplify (x^2+3x+2)/(x^2-4x-12)

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

Step 1

Factor $x^{2} + 3 x + 2$ 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 $2$ and whose sum is $3$ .

$1, 2$

Write the factored form using these integers.

$\frac{(x + 1) (x + 2)}{x^{2} - 4 x - 12}$

Step 2

Factor $x^{2} - 4 x - 12$ 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 $- 4$ .

$- 6, 2$

Write the factored form using these integers.

$\frac{(x + 1) (x + 2)}{(x - 6) (x + 2)}$

Step 3

Cancel the common factor of $x + 2$ .

Cancel the common factor.

$\frac{(x + 1) (x + 2)}{(x - 6) (x + 2)}$

Rewrite the expression.

$\frac{x + 1}{x - 6}$

Simplify (x^2+3x+2)/(x^2-4x-12)

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