Simplify (x^2+8x+15)/(x^2-3x-18)

$\frac{x^{2} + 8 x + 15}{x^{2} - 3 x - 18}$

Step 1

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.

$\frac{(x + 3) (x + 5)}{x^{2} - 3 x - 18}$

Step 2

Factor $x^{2} - 3 x - 18$ 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 $- 18$ and whose sum is $- 3$ .

$- 6, 3$

Write the factored form using these integers.

$\frac{(x + 3) (x + 5)}{(x - 6) (x + 3)}$

Step 3

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{(x + 3) (x + 5)}{(x - 6) (x + 3)}$

Rewrite the expression.

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

Simplify (x^2+8x+15)/(x^2-3x-18)

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