What is (x^{-1}-y^{-1})/(x^{-1)+y^{-1}} ?

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

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simplify (x^{-1}-y^{-1})/(x^{-1)+y^{-1}}

simplify

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

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

Solution steps

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

Simplify

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

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

Simplify

x^{- 1} + y^{- 1} : \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}

7 x^{2} + 8 x = - 6

4 - 2 a

e^{- \frac{x}{10}} < 0.1

2 x^{2} - 8 x - 10 = 32

2 x - 1 > 0

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