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

The solution to (x^{-1}+y^{-1})/((x+y)^{-1)} is ((y+x)^2)/(xy)

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

simplify

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

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

Solution steps

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

Simplify

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

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

Apply the fraction rule:

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

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

Apply the commutative law:

x + y = y + x

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

Simplify

\frac{y + x}{( y + x ) ^{- 1}} : (y + x)^{2}

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

- 6 x^{2} - 15 x + 9

\frac{- \frac{π}{3} + \frac{2 π}{3}}{2}

\frac{1}{x ^{2} + x} \geq \frac{1}{x ^{2} - x} - \frac{1}{x ^{2} - x}

350 \leq 5.5 t - 110

12 x - 9 = 6 x + 39

What is (x^{-1}+y^{-1})/((x+y)^{-1)} ?
The solution to (x^{-1}+y^{-1})/((x+y)^{-1)} is ((y+x)^2)/(xy)