Question

What should be added to $\frac{a}{a-b}+\frac{b}{a+b}$ to get 1?

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

Answer 1

The correct option is C $\frac{2ab}{b^2-a^2}$

Reqd exp = $1-[\frac{a}{a-b}+\frac{b}{a+b}]$
= $1-\left[\frac{a(a+b)+b(a-b)}{a^2-b^2}\right]$
= $1-\left[\frac{a^2+ab+ab-b^2}{a^2-b^2}\right]$
= $\frac{(a^2-b^2)-(a^2+2ab-b^2)}{a^2-b^2}$
= $\frac{-2ab}{a^2-b^2}=\frac{2ab}{b^2-a^2}$