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Popular >

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

Solution

simplify

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

Solution

\frac{1}{x - 1}

Solution steps

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

Join

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

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

Join

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

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

Cancel

\frac{( x + 1 ) x}{x ( x ^{2} - 1 )} : \frac{1}{x - 1}

= \frac{1}{x - 1}

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Frequently Asked Questions (FAQ)

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