Question

Of the following expressions, the one equal to $\frac{a^{-1}{b}^{-1}}{a^{-3}-b^{-3}}$ is:

• A. $\frac{a^2{b}^2}{b^2-a^2}$
• B. $\frac{a^2{b}^2}{b^3-a^3}$
• C. $\frac{ab}{b^3-a^3}$
• D. $\frac{a^3-b^3}{ab}$

Answer 1

The correct option is B $\frac{a^2{b}^2}{b^3-a^3}$

$\frac{a^{-1}{b}^{-1}}{a^{-3}-b^{-3}}=\frac{\frac{1}{ab}}{\frac{1}{a^3}-\frac{1}{b^3}}=\frac{\frac{1}{ab}}{\frac{b^3-a^3}{a^3{b}^3}}=\frac{a^3{b}^3\frac{1}{ab}}{b^3-a^3}=\frac{a^2{b}^2}{b^3-a^3}$