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

Aug 13, 2016

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

#### Explanation:

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

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

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

$\text{We can write as "-(x+5)/((x-5)(x+5))" so } \left({x}^{2} - {5}^{2}\right) = \left(x - 5\right) \left(x + 5\right)$

-cancel(x+5)/((x-5)* cancel((x+5))

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

Aug 13, 2016

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

#### Explanation:

The first step in most algebraic fraction problems is to find factors.

$\frac{x + 5}{x - 5} \textcolor{red}{\div} \frac{\textcolor{m a \ge n t a}{{x}^{2} - 25}}{5 - x} \text{ "color(magenta)(x^2-25)"( difference of squares)}$

=(x+5)/(x-5) color(red)(xx)color(blue)((5-x))/(color(magenta)((x+5)(x-5))

NOTE: $\textcolor{b l u e}{\left(5 - x\right) = - \left(x - 5\right)}$

=cancel(x+5)/cancel(x-5) color(red)(xx)color(blue)((-cancel((x-5)^1))/(cancel((x+5))(x-5)

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

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