Simplify (12x+36)/(x^2-4x-21)

$\frac{12 x + 36}{x^{2} - 4 x - 21}$

Step 1

Factor $12$ out of $12 x + 36$ .

Factor $12$ out of $12 x$ .

$\frac{12 (x) + 36}{x^{2} - 4 x - 21}$

Factor $12$ out of $36$ .

$\frac{12 x + 12 \cdot 3}{x^{2} - 4 x - 21}$

Factor $12$ out of $12 x + 12 \cdot 3$ .

$\frac{12 (x + 3)}{x^{2} - 4 x - 21}$

Step 2

Factor $x^{2} - 4 x - 21$ 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 $- 21$ and whose sum is $- 4$ .

$- 7, 3$

Write the factored form using these integers.

$\frac{12 (x + 3)}{(x - 7) (x + 3)}$

Step 3

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{12 (x + 3)}{(x - 7) (x + 3)}$

Rewrite the expression.

$\frac{12}{x - 7}$

Simplify (12x+36)/(x^2-4x-21)

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