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

The solution to (1/(x-1)-1)/(1/(x-1)+1) is (-x+2)/x

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

simplify

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

\frac{- x + 2}{x}

Solution steps

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

Join

\frac{1}{x - 1} - 1 : \frac{- x + 2}{x - 1}

= \frac{\frac{- x + 2}{x - 1}}{\frac{1}{x - 1} + 1}

Join

\frac{1}{x - 1} + 1 : \frac{x}{x - 1}

= \frac{\frac{- x + 2}{x - 1}}{\frac{x}{x - 1}}

Apply the fraction rule:

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

= \frac{( - x + 2 ) ( x - 1 )}{( x - 1 ) x}

Cancel the common factor:

x - 1

= \frac{- x + 2}{x}

12 - 2 + 8 - 3

3 + \frac{3}{x + 3}

- 2^{\frac{3}{2}}

(- b)^{2}

4 \cdot 48

What is (1/(x-1)-1)/(1/(x-1)+1) ?
The solution to (1/(x-1)-1)/(1/(x-1)+1) is (-x+2)/x