Problem: The fraction a−4−b−4a−2−b−2\dfrac{a^{-4}-b^{-4}}{a^{-2}-b^{-2}}a−2−b−2a−4−b−4 is equal to:
Answer Choices:
A. a−6−b−6a^{-6}-b^{-6}a−6−b−6
B. a−2−b−2a^{-2}-b^{-2}a−2−b−2
C. a−2+b−2a^{-2}+b^{-2}a−2+b−2
D. a2+b2a^{2}+b^{2}a2+b2
E. a2−b2a^{2}-b^{2}a2−b2 Solution:
(a−2+b−2)(a−2−b−2)a−2−b−2=a−2+b−2\dfrac{\left(a^{-2}+b^{-2}\right)\left(a^{-2}-b^{-2}\right)}{a^{-2}-b^{-2}}=a^{-2}+b^{-2}a−2−b−2(a−2+b−2)(a−2−b−2)=a−2+b−2.