What is the value of $\frac{\frac{1}{5} - \frac{1}{x}}{\frac{5}{x} - 1}$ $(1/5-1/x)/(5/x-1)$ ?

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Answer 1 · 2015-05-28T13:28:20

$- \frac{1}{5}$ $color(lime)(-1/5)$

$\frac{\frac{1}{5} - \frac{1}{x}}{\frac{5}{x} - 1}$ $(color(red)(1/5-1/x))/(color(blue)(5/x-1))$

$= \frac{\frac{x - 5}{5 x}}{\frac{5 - x}{x}}$ $= (color(red)((x-5)/(5x)))/(color(blue)((5-x)/x))$

$= \frac{x - 5}{5 x} \cdot \frac{x}{5 - x}$ $= color(red)((x-5)/(5x)) * color(blue)(x/(5-x))$

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

What is the value of (1/5-1/x)/(5/x-1)15−1x5x−1(1/5-1/x)/(5/x-1)?