Simplify x/(x+5)*(x^2-25)/(2x)

$\frac{x}{x + 5} \cdot \frac{x^{2} - 25}{2 x}$

Step 1

Simplify the numerator.

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

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

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 $b = 5$ .

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

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x$ .

Factor $x$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{x + 5} \cdot \frac{(x + 5) (x - 5)}{2}$

Cancel the common factor of $x + 5$ .

Cancel the common factor.

$\frac{1}{x + 5} \cdot \frac{(x + 5) (x - 5)}{2}$

Rewrite the expression.

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