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

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

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

simplify

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

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

Solution steps

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

Join

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

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

Join

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

\frac{16}{3} + 4

\frac{x}{2} + 2 x

- x^{2} - 4 x - 7

36 \times 7

- 1 \times 9