Simplify (x^2+2x-24)/(x^2+7x+6)

$\frac{x^{2} + 2 x - 24}{x^{2} + 7 x + 6}$

Step 1

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

$- 4, 6$

Write the factored form using these integers.

$\frac{(x - 4) (x + 6)}{x^{2} + 7 x + 6}$

Step 2

Factor $x^{2} + 7 x + 6$ 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 $7$ .

$1, 6$

Write the factored form using these integers.

$\frac{(x - 4) (x + 6)}{(x + 1) (x + 6)}$

Step 3

Cancel the common factor of $x + 6$ .

Cancel the common factor.

$\frac{(x - 4) (x + 6)}{(x + 1) (x + 6)}$

Rewrite the expression.

$\frac{x - 4}{x + 1}$

Simplify (x^2+2x-24)/(x^2+7x+6)

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