Simplify (q^2+11q+24)/(q^2-5q-24)

$\frac{q^{2} + 11 q + 24}{q^{2} - 5 q - 24}$

Step 1

Factor $q^{2} + 11 q + 24$ 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 $24$ and whose sum is $11$ .

$3, 8$

Write the factored form using these integers.

$\frac{(q + 3) (q + 8)}{q^{2} - 5 q - 24}$

Step 2

Factor $q^{2} - 5 q - 24$ 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 $- 24$ and whose sum is $- 5$ .

$- 8, 3$

Write the factored form using these integers.

$\frac{(q + 3) (q + 8)}{(q - 8) (q + 3)}$

Step 3

Cancel the common factor of $q + 3$ .

Cancel the common factor.

$\frac{(q + 3) (q + 8)}{(q - 8) (q + 3)}$

Rewrite the expression.

$\frac{q + 8}{q - 8}$

Simplify (q^2+11q+24)/(q^2-5q-24)

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