# How do you simplify (x+5 )/ (x^2-25)?

##### 2 Answers
Jun 22, 2018

$\frac{1}{x - 5}$

#### Explanation:

${x}^{2} - 25 \text{ is a "color(blue)"difference of squares}$

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

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

$\frac{\cancel{\left(x + 5\right)}}{\cancel{\left(x + 5\right)} \left(x - 5\right)} = \frac{1}{x - 5}$

$\text{with restriction } x \ne 5$

Jun 22, 2018

$\frac{1}{x - 5}$

#### Explanation:

The key realization is that our denominator fits the difference of squares pattern ${a}^{2} - {b}^{2}$, which factors as $\left(a + b\right) \left(a - b\right)$.

We can rewrite ${x}^{2} - 25$ as $\left(x + 5\right) \left(x - 5\right)$, which allows us to rewrite our original expression as

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

The $x + 5$ terms on the top and bottom cancel, and we're left with

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

$\frac{1}{x - 5}$

Hope this helps!