Question

State true or false.

The simplest form of $(a^{-1}+b^{-1})÷(a^{-2}-b^{-2})$ is equal to $\frac{ab}{b-a}$.

• A. True
• B. False

Answer 1

The correct option is A True

$(a^{-1}+b^{-1})÷(a^{-2}-b^{-2})$

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

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

$=\frac{\frac{a+b}{ab}}{\frac{(a+b)(b-a)}{a^2{b}^2}}$

$=\frac{ab}{b-a}$

The given statement is true.