Simplify (x^2+x-6)/(x^2+8x+15)

$\frac{x^{2} + x - 6}{x^{2} + 8 x + 15}$

Step 1

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 $1$ .

$- 2, 3$

Write the factored form using these integers.

$\frac{(x - 2) (x + 3)}{x^{2} + 8 x + 15}$

Step 2

Factor $x^{2} + 8 x + 15$ 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 $15$ and whose sum is $8$ .

$3, 5$

Write the factored form using these integers.

$\frac{(x - 2) (x + 3)}{(x + 3) (x + 5)}$

Step 3

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{(x - 2) (x + 3)}{(x + 3) (x + 5)}$

Rewrite the expression.

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

Simplify (x^2+x-6)/(x^2+8x+15)

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