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

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

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

simplify

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

\frac{1}{x y}

Solution steps

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

Simplify

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

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

Apply the fraction rule:

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

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

Cancel

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

= \frac{1}{x y}

(x + 1) - 1

(s + 1) (s^{2} + 6 s + 13)

15 m^{2} + m - 6

\frac{- 5}{10}

- x^{3} + 4 x^{2} - x - 6