Simplify (x^2+x-12)/(x^2-8x+15)*(2x^2-10x)/(5x+20)

$\frac{x^{2} + x - 12}{x^{2} - 8 x + 15} \cdot \frac{2 x^{2} - 10 x}{5 x + 20}$

Step 1

Factor $x^{2} + x - 12$ 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 $- 12$ and whose sum is $1$ .

$- 3, 4$

Write the factored form using these integers.

$\frac{(x - 3) (x + 4)}{x^{2} - 8 x + 15} \cdot \frac{2 x^{2} - 10 x}{5 x + 20}$

Step 2

Factor $x^{2} - 8 x + 15$ 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 $15$ and whose sum is $- 8$ .

$- 5, - 3$

Write the factored form using these integers.

$\frac{(x - 3) (x + 4)}{(x - 5) (x - 3)} \cdot \frac{2 x^{2} - 10 x}{5 x + 20}$

Step 3

Simplify terms.

Factor $2 x$ out of $2 x^{2} - 10 x$ .

Factor $2 x$ out of $2 x^{2}$ .

$\frac{(x - 3) (x + 4)}{(x - 5) (x - 3)} \cdot \frac{2 x (x) - 10 x}{5 x + 20}$

Factor $2 x$ out of $- 10 x$ .

$\frac{(x - 3) (x + 4)}{(x - 5) (x - 3)} \cdot \frac{2 x (x) + 2 x (- 5)}{5 x + 20}$

Factor $2 x$ out of $2 x (x) + 2 x (- 5)$ .

$\frac{(x - 3) (x + 4)}{(x - 5) (x - 3)} \cdot \frac{2 x (x - 5)}{5 x + 20}$

Factor $5$ out of $5 x + 20$ .

Factor $5$ out of $5 x$ .

$\frac{(x - 3) (x + 4)}{(x - 5) (x - 3)} \cdot \frac{2 x (x - 5)}{5 (x) + 20}$

Factor $5$ out of $20$ .

$\frac{(x - 3) (x + 4)}{(x - 5) (x - 3)} \cdot \frac{2 x (x - 5)}{5 x + 5 \cdot 4}$

Factor $5$ out of $5 x + 5 \cdot 4$ .

$\frac{(x - 3) (x + 4)}{(x - 5) (x - 3)} \cdot \frac{2 x (x - 5)}{5 (x + 4)}$

Cancel the common factor of $x + 4$ .

Factor $x + 4$ out of $(x - 3) (x + 4)$ .

$\frac{(x + 4) (x - 3)}{(x - 5) (x - 3)} \cdot \frac{2 x (x - 5)}{5 (x + 4)}$

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

$\frac{(x + 4) (x - 3)}{(x - 5) (x - 3)} \cdot \frac{2 x (x - 5)}{(x + 4) \cdot 5}$

Cancel the common factor.

$\frac{(x + 4) (x - 3)}{(x - 5) (x - 3)} \cdot \frac{2 x (x - 5)}{(x + 4) \cdot 5}$

Rewrite the expression.

$\frac{x - 3}{(x - 5) (x - 3)} \cdot \frac{2 x (x - 5)}{5}$

Cancel the common factor of $x - 5$ .

Factor $x - 5$ out of $2 x (x - 5)$ .

$\frac{x - 3}{(x - 5) (x - 3)} \cdot \frac{(x - 5) (2 x)}{5}$

Cancel the common factor.

$\frac{x - 3}{(x - 5) (x - 3)} \cdot \frac{(x - 5) (2 x)}{5}$

Rewrite the expression.

$\frac{x - 3}{x - 3} \cdot \frac{2 x}{5}$

Multiply $\frac{x - 3}{x - 3}$ by $\frac{2 x}{5}$ .

$\frac{(x - 3) (2 x)}{(x - 3) \cdot 5}$

Cancel the common factor of $x - 3$ .

Cancel the common factor.

$\frac{(x - 3) (2 x)}{(x - 3) \cdot 5}$

Rewrite the expression.

$\frac{2 x}{5}$

Simplify (x^2+x-12)/(x^2-8x+15)*(2x^2-10x)/(5x+20)

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