Simplify (x^2+5x+6)/(x^2-x-6)

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

Step 1

Factor $x^{2} + 5 x + 6$ 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 $6$ and whose sum is $5$ .

$2, 3$

Write the factored form using these integers.

$\frac{(x + 2) (x + 3)}{x^{2} - x - 6}$

Step 2

Factor $x^{2} - x - 6$ 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 $- 6$ and whose sum is $- 1$ .

$- 3, 2$

Write the factored form using these integers.

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

Step 3

Cancel the common factor of $x + 2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify (x^2+5x+6)/(x^2-x-6)

Related Questions

Support LCMGCF.com by disabling your adblocker.