What is the value of (1/5-1/x)/(5/x-1)?

May 28, 2015

$\textcolor{\lim e}{- \frac{1}{5}}$

Explanation:

$\frac{\textcolor{red}{\frac{1}{5} - \frac{1}{x}}}{\textcolor{b l u e}{\frac{5}{x} - 1}}$

$= \frac{\textcolor{red}{\frac{x - 5}{5 x}}}{\textcolor{b l u e}{\frac{5 - x}{x}}}$

$= \textcolor{red}{\frac{x - 5}{5 x}} \cdot \textcolor{b l u e}{\frac{x}{5 - x}}$

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