Simplify 6/(x^2+9x+20)*(8x+40)/(6x-12)

$\frac{6}{x^{2} + 9 x + 20} \cdot \frac{8 x + 40}{6 x - 12}$

Factor $x^{2} + 9 x + 20$ 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 $20$ and whose sum is $9$ .

$4, 5$

Write the factored form using these integers.

$\frac{6}{(x + 4) (x + 5)} \cdot \frac{8 x + 40}{6 x - 12}$

Simplify terms.

Factor $8$ out of $8 x + 40$ .

Factor $8$ out of $8 x$ .

$\frac{6}{(x + 4) (x + 5)} \cdot \frac{8 (x) + 40}{6 x - 12}$

Factor $8$ out of $40$ .

$\frac{6}{(x + 4) (x + 5)} \cdot \frac{8 x + 8 \cdot 5}{6 x - 12}$

Factor $8$ out of $8 x + 8 \cdot 5$ .

$\frac{6}{(x + 4) (x + 5)} \cdot \frac{8 (x + 5)}{6 x - 12}$

Factor $6$ out of $6 x - 12$ .

Factor $6$ out of $6 x$ .

$\frac{6}{(x + 4) (x + 5)} \cdot \frac{8 (x + 5)}{6 (x) - 12}$

Factor $6$ out of $- 12$ .

$\frac{6}{(x + 4) (x + 5)} \cdot \frac{8 (x + 5)}{6 x + 6 \cdot - 2}$

Factor $6$ out of $6 x + 6 \cdot - 2$ .

$\frac{6}{(x + 4) (x + 5)} \cdot \frac{8 (x + 5)}{6 (x - 2)}$

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6}{(x + 4) (x + 5)} \cdot \frac{8 (x + 5)}{6 (x - 2)}$

Rewrite the expression.

$\frac{1}{(x + 4) (x + 5)} \cdot \frac{8 (x + 5)}{x - 2}$

Cancel the common factor of $x + 5$ .

Factor $x + 5$ out of $(x + 4) (x + 5)$ .

$\frac{1}{(x + 5) (x + 4)} \cdot \frac{8 (x + 5)}{x - 2}$

Factor $x + 5$ out of $8 (x + 5)$ .

$\frac{1}{(x + 5) (x + 4)} \cdot \frac{(x + 5) \cdot 8}{x - 2}$

Cancel the common factor.

$\frac{1}{(x + 5) (x + 4)} \cdot \frac{(x + 5) \cdot 8}{x - 2}$

Rewrite the expression.

$\frac{1}{x + 4} \cdot \frac{8}{x - 2}$

Multiply $\frac{1}{x + 4}$ by $\frac{8}{x - 2}$ .

$\frac{8}{(x + 4) (x - 2)}$

Simplify 6/(x^2+9x+20)*(8x+40)/(6x-12)

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