$\frac{a^{- 4} - b^{- 4}}{a^{- 2} - b^{- 2}}$ is same as

\frac{b^{2} - a^{2}}{a^{2} b^{2}}

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\frac{b^{2} + a^{2}}{a^{2} b^{2}}

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\frac{a^{2} b^{2}}{a^{2} + b^{2}}

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\frac{a^{2} b^{2}}{b^{2} - a^{2}}

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Solution

The correct option is B $\frac{b^{2} + a^{2}}{a^{2} b^{2}}$
$\frac{a^{- 4} - b^{- 4}}{a^{- 2} - b^{- 2}}$
$= \frac{\frac{1}{a^{4}} - \frac{1}{b^{4}}}{\frac{1}{a^{2}} - \frac{1}{b^{2}}}$
$= \frac{\frac{b^{4} - a^{4}}{a^{4} b^{4}}}{\frac{b^{2} - a^{2}}{a^{2} b^{2}}}$
$= \frac{\frac{(b^{2} - a^{2}) (b^{2} + a^{2})}{a^{4} b^{4}}}{\frac{b^{2} - a^{2}}{a^{2} b^{2}}}$
$= \frac{\frac{(b^{2} + a^{2})}{a^{4} b^{4}}}{\frac{1}{a^{2} b^{2}}}$
$= \frac{a^{2} b^{2} (b^{2} + a^{2})}{a^{4} b^{4}}$
$= \frac{a^{2} + b^{2}}{a^{2} b^{2}}$

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