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Popular >

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

Solution

simplify

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

Solution

x - y

Solution steps

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

Join

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

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

Join

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

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

Apply the fraction rule:

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

= \frac{( x ^{2} - y ^{2} ) x y}{x y ( x + y )}

Cancel

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

= x - y

Popular Examples

x^{2} - 12 x + 32 > 0

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81 \cdot 36

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(- \frac{2}{9 - y})^{2}

factor 24c^5-12c^3 factor

24 c^{5} - 12 c^{3}

2 - x^{2} - x = 0

Frequently Asked Questions (FAQ)

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