Simplify (x^2-8x-20)/(x-10)*(3x)/(x+2)

$\frac{x^{2} - 8 x - 20}{x - 10} \cdot \frac{3 x}{x + 2}$

Step 1

Factor $x^{2} - 8 x - 20$ 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 $- 8$ .

$- 10, 2$

Write the factored form using these integers.

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

Step 2

Simplify terms.

Cancel the common factor of $x + 2$ .

Factor $x + 2$ out of $(x - 10) (x + 2)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x - 10}{x - 10} \cdot (3 x)$

Combine $3$ and $\frac{x - 10}{x - 10}$ .

$\frac{3 (x - 10)}{x - 10} \cdot x$

Combine $\frac{3 (x - 10)}{x - 10}$ and $x$ .

$\frac{3 (x - 10) x}{x - 10}$

Cancel the common factor of $x - 10$ .

Cancel the common factor.

$\frac{3 (x - 10) x}{x - 10}$

Divide $3 x$ by $1$ .

$3 x$

Simplify (x^2-8x-20)/(x-10)*(3x)/(x+2)

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