Simplify (x^2-2x-15)/(x^2(x+3))*(x(x+2))/(x-5)

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

Step 1

Factor $x^{2} - 2 x - 15$ 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 $- 2$ .

$- 5, 3$

Write the factored form using these integers.

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

Step 2

Simplify terms.

Cancel the common factor of $x - 5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ .

Factor $x$ out of $x^{2} (x + 3)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x + 3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{x} \cdot (x + 2)$

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

$\frac{x + 2}{x}$

Simplify (x^2-2x-15)/(x^2(x+3))*(x(x+2))/(x-5)

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