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

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

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

simplify

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

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

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}}

Apply the fraction rule:

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

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

Join

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

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

Multiply

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

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

Apply the fraction rule:

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

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

2^{n (a) \cdot n (b)}

\frac{3 x ^{- 5}}{( 2 x ^{- 2} )}

(d^{2} + 1)^{3}

5 x^{3} (4 x^{2} + 3 x + 7)

\frac{lo g _{10} ( 1 )}{100 x ^{1000}}

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