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}

\frac{12}{24}

(- 8 + 8 i) + (2 - i)

- 10 (a + 2)

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)