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

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

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

simplify

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

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

Solution steps

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

Simplify

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

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

Join

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

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

Simplify

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

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

Join

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

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

Divide fractions:

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

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

Cancel the common factor:

y^{2}

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

Cancel the common factor:

x^{2}

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

∣ x - 6 ∣ = 2

\frac{7}{x} > 6

(x - 2)^{4} (3 x + 2)^{3} - 10 (x - 2) + 9

52 t - 16 t^{2}

2 r - 1 > 17

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