Simplify ((x^2-25)/(x-5))÷(x-5)

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

Rewrite the division as a fraction.

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

Multiply the numerator by the reciprocal of the denominator.

$\frac{x^{2} - 25}{x - 5} \cdot \frac{1}{x - 5}$

Simplify the numerator.

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

$\frac{x^{2} - 5^{2}}{x - 5} \cdot \frac{1}{x - 5}$

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 $b = 5$ .

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

Cancel the common factor of $x - 5$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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