Simplify : $(a^{-1} + b^{-1}) ÷ (a^{-3}+b^{-3})$
Answer & explanation
Correct answer: option 4
We know that,
a3 + b3 = ( a + b ) ( a2 + b2 - ab )
So, $(a^{-1} + b^{-1}) ÷ (a^{-3}+b^{-3})$
= \(\frac{\frac{a + b}{ab}}{\frac{a^3 + b^3}{a^3b^3}}\)
= \(\frac{\frac{a + b}{ab}}{\frac{ ( a + b ) ( a^2+ b^2- ab )}{a^3b^3}}\)
= $\frac{a^2b^2}{(a^2-ab+b^2)}$