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

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

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

simplify

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

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

Solution steps

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

Join

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

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

Join

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

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

Apply the fraction rule:

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

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

Cancel the common factor:

x

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

f (a t)

\frac{1}{4} \times (- 2)

\frac{2 x ^{3} y ^{- 2} z ^{5}}{x ^{2} y z ^{3}}

4 x (x + 1)

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