What is (x/(x-1))/(x/(x-1)-1) ?

The solution to (x/(x-1))/(x/(x-1)-1) is x

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simplify (x/(x-1))/(x/(x-1)-1)

simplify

\frac{\frac{x}{x - 1}}{\frac{x}{x - 1} - 1}

x

Solution steps

\frac{\frac{x}{x - 1}}{\frac{x}{x - 1} - 1}

Apply the fraction rule:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

= \frac{x}{( x - 1 ) ( \frac{x}{x - 1} - 1 )}

Cancel

\frac{x}{( x - 1 ) ( \frac{x}{x - 1} - 1 )} : x

= x

\frac{24}{- 8}

\frac{- b}{2 a}

(s - 1)^{2} + 1

1 + \frac{2 b}{3} + \frac{b ^{2}}{9}

\frac{15 a ^{3} b ^{2}}{20 a b ^{4}}