Question

If $\frac{a^2+2ab+b^2}{a^2-b^2}=2a+2b$, what is the value of $a-b$?

• A. $1$
• B. $-1$
• C. $2$
• D. $\frac{1}{2}$
• E. $-\frac{1}{2}$

Answer 1

The correct option is D $\frac{1}{2}$

Given, $\frac{a^2+2ab+b^2}{a^2-b^2}=2a+2b$
$\Rightarrow \frac{{(a+b)}^2}{(a+b)(a-b)}=2(a+b)$
$\Rightarrow (a+b)=2(a+b)(a-b)$
$\Rightarrow 2(a-b)=1$
$\Rightarrow a-b=\frac{1}{2}$