The fraction a^-4-b^-4a^-2-b^-2 is equal to:

1955 AMC 12 Problem 13

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13.

The fraction

\dfrac{a^{-4}-b^{-4}}{a^{-2}-b^{-2}}

is equal to:

a^{-6}-b^{-6}

a^{-2}-b^{-2}

a^{-2}+b^{-2}

a^2+b^2

a^2-b^2

Regard

a^{-4}-b^{-4}

as a difference of squares

Factor it using

a^{-2}

and

b^{-2}

Factoring the numerator,

\begin{aligned} a^{-4}-b^{-4} &=(a^{-2}-b^{-2})\\ &\quad\cdot(a^{-2}+b^{-2}). \end{aligned}

Where the original fraction is defined, canceling the common factor leaves

a^{-2}+b^{-2}.

Thus, the correct answer is C.