Simplify (x^2-25)/(x^2-2x-15)*(x+3)/x

$\frac{x^{2} - 25}{x^{2} - 2 x - 15} \cdot \frac{x + 3}{x}$

Step 1

Simplify the numerator.

Rewrite $25$ as $5^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 5$ .

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

Step 2

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.

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

Step 3

Simplify terms.

Cancel the common factor of $x + 3$ .

Factor $x + 3$ out of $(x - 5) (x + 3)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{(x + 5) (x - 5)}{x - 5}$ by $\frac{1}{x}$ .

$\frac{(x + 5) (x - 5)}{(x - 5) x}$

Cancel the common factor of $x - 5$ .

Cancel the common factor.

$\frac{(x + 5) (x - 5)}{(x - 5) x}$

Rewrite the expression.

$\frac{x + 5}{x}$

Simplify (x^2-25)/(x^2-2x-15)*(x+3)/x

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