Question : If $\frac{x}{a+b}+1=\frac{x}{a-b}+\frac{a-b}{a+b}$, then $x$ is equal to:
Option 1: $2a-b$
Option 2: $a+b$
Option 3: $a-b$
Option 4: $2a+b$
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Correct Answer: $a-b$
Solution :
Given:
$\frac{x}{a+b}+1=\frac{x}{a-b}+\frac{a-b}{a+b}$
⇒ $\frac{x}{a+b}-\frac{x}{a-b}=\frac{a-b}{a+b}-1$
⇒ $x(\frac{1}{a+b}-\frac{1}{a-b})=\frac{-2b}{a+b}$
⇒ $x(\frac{-2b}{(a+b)(a-b)})=\frac{-2b}{a+b}$
⇒ $x=(a-b)$
Hence, the correct answer is $(a-b)$.
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