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

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

Step 1

Factor $x$ out of $x^{2} - 5 x$ .

Factor $x$ out of $x^{2}$ .

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

Factor $x$ out of $- 5 x$ .

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

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

$\frac{x (x - 5)}{x^{2} - 25}$

Step 2

Simplify the denominator.

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

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

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 $b = 5$ .

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

Step 3

Cancel the common factor of $x - 5$ .

Cancel the common factor.

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

Rewrite the expression.

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