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

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

Step 1

Factor $x^{2} + 11 x + 24$ 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.

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

Step 2

Factor $x^{2} - 5 x - 24$ 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.

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

Step 3

Cancel the common factor of $x + 3$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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