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

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

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

simplify

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

\frac{y - x}{y + x}

Solution steps

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

Join

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

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

Join

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

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

Apply the fraction rule:

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

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

Cancel

\frac{( y - x ) x y}{x y ( y + x )} : \frac{y - x}{y + x}

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

2 x^{2} - x^{3}

3 m^{5} n^{2} - 6 m^{4} n + m^{3}

\frac{1}{3 - 2}

x = 2^{2}

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