What is factor (x^{-1}+y^{-1})/(x^{-2)-y^{-2}} ?

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

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factor (x^{-1}+y^{-1})/(x^{-2)-y^{-2}}

factor

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

\frac{x y}{y - x}

Solution steps

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

Simplify

x^{- 2} - y^{- 2} : \frac{1}{x ^{2}} - \frac{1}{y ^{2}}

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

Join

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

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

Simplify

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

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

Join

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

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

Divide fractions:

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

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

Cancel the common factor:

y + x

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

Cancel the common factor:

x

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

Cancel the common factor:

y

= \frac{x y}{y - x}

r^{2} + 20 r + 100

7 x - 4 + x = - 1 + 13 x + 7

1.4 = \frac{t}{1.5}

\frac{5 u}{5 uv - 30 u w}

9 x^{2} - 17 x - 2

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