# What is the simplified form of (x^2-25)/(x-5)?

Sep 13, 2015

$\frac{{x}^{2} - 25}{x - 5} = x + 5$ with exclusion $x \ne 5$

#### Explanation:

Use the difference of squares identity:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

to find:

$\frac{{x}^{2} - 25}{x - 5} = \frac{{x}^{2} - {5}^{2}}{x - 5} = \frac{\left(x - 5\right) \left(x + 5\right)}{x - 5}$

$= \frac{x - 5}{x - 5} \cdot \left(x + 5\right) = x + 5$

with exclusion $x \ne 5$

Note that if $x = 5$ then both $\left({x}^{2} - 25\right)$ and $\left(x - 5\right)$ are $0$, so $\frac{{x}^{2} - 25}{x - 5} = \frac{0}{0}$ is undefined.