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

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

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simplify (x^{-2}-y^{-2})/(x^{-1)-y^{-1}}

simplify

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

\frac{y + x}{x y}

Solution steps

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

Simplify

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

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

Join

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

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

Simplify

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

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

Join

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

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

Divide fractions:

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

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

Cancel

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

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

Apply Difference of Two Squares Formula:

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

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

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

Cancel the common factor:

y - x

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

74

v^{2} + 5 v + 4

lo g_{10} (- 2)

(\frac{32}{5})^{- 2 x}

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