Simplify (x^2+7x+12)/(x-5)*(2x-10)/(x+3)

$\frac{x^{2} + 7 x + 12}{x - 5} \cdot \frac{2 x - 10}{x + 3}$

Step 1

Factor $x^{2} + 7 x + 12$ 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 $7$ .

$3, 4$

Write the factored form using these integers.

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

Step 2

Simplify terms.

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

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $- 10$ .

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

Factor $2$ out of $2 x + 2 \cdot - 5$ .

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

Cancel the common factor of $x + 3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 5$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

$(x + 4) \cdot 2$

Apply the distributive property.

$x \cdot 2 + 4 \cdot 2$

Simplify the expression.

Move $2$ to the left of $x$ .

$2 \cdot x + 4 \cdot 2$

Multiply $4$ by $2$ .

$2 x + 8$

Simplify (x^2+7x+12)/(x-5)*(2x-10)/(x+3)

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