Question

pleas solve this problem​

Answer 1

$\mathsf{\dfrac{x}{a+b}+1=\dfrac{x}{a-b}+\dfrac{a-b}{a+b}}\\ \\ \\ \mathsf{\dfrac{x}{a+b}-\dfrac{x}{a-b}=\dfrac{a-b}{a+b}-1}\\ \\ \\ \mathsf{x\left(\dfrac{1}{a+b}-\dfrac{1}{a-b}\right)=\dfrac{a-b-(a+b)}{a+b}}\\ \\ \\ \mathsf{x\left(\dfrac{a-b-(a+b)}{(a+b)(a-b)}\right)=\dfrac{a-b-a-b}{a+b}}\\ \\ \\ \mathsf{x\cdot \dfrac{-2b}{(a+b)(a-b)}=\dfrac{-2b}{a+b}}\\ \\ \\ \mathsf{x\cdot \dfrac{-2b}{a+b}\cdot \dfrac{1}{a-b}=\dfrac{-2b}{a+b}}\\ \\ \\ \mathsf{\dfrac{x}{a-b}=1}\\ \\ \\ \Large\textsf{x = a - b}$

$\text{Hence the answer is}\ \ \mathsf{x=a-b}. \\ \\ \\ \text{Let's check!}\\ \\ \\ \mathsf{LHS  = \dfrac{x}{a+b}+1= \dfrac{a-b}{a+b}+1=1+\dfrac{a-b}{a+b}}\\ \\ \\ \mathsf{=\dfrac{a-b}{a-b}+\dfrac{a-b}{a+b}=\dfrac{x}{a-b}+\dfrac{a-b}{a+b}=RHS}$

$\text{Hence Checked!!!}$