Question

(a+x-2b/2a-b)-(a-2b/x)=1​

Answer 1

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

$\implies\displaystyle\frac{x(a+x-2b)-(2a-b)(a-2b)}{(2a-b)x}=1$

$\implies\displaystyle\;x(a+x-2b)-(2a-b)(a-2b)=(2a-b)x$

$\implies\displaystyle\;x^2+(a-2b)x-(2a-b)(a-2b)=(2a-b)x$

$\implies\displaystyle\;x^2+(a-2b)x-(2a-b)x-(2a-b)(a-2b)=0$

$\implies\displaystyle\;x(x+(a-2b))-(2a-b)(x+(a-2b))=0$

$\implies\displaystyle\;(x-(2a-b))(x+(a-2b))=0$

$\implies\displaystyle\;x=2a-b,\;-(a-2b)$

$\therefore\textbf{The solution is 2a-b and -(a-2b) }$