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

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

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

simplify

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

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

Solution steps

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

Simplify

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

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

Join

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

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

Simplify

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

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

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 ^{2} - x ^{2}}{x ^{2} y ^{2}}}

Divide fractions:

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

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

Cancel the common factor:

x^{2}

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

Cancel the common factor:

y^{2}

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

y^{2} + 11 y + 14 = 0

e^{x} - 12 e^{- x} - 1 = 0

(5 x + 9) = (7 x - 9)

3 a^{- 1}

∣ 2 x + 6 ∣ - 4 = 20

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