Question

Solve the following quadratic equation by factorization :
$\frac{1}{2a+b+2x}=\frac{1}{2a}+\frac{1}{b}+\frac{1}{2x}$

Answer 1

Consider the given equation.

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

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

$\frac{2x-(2a+b+2x)}{(2a+b+2x)2x}=\frac{2a+b}{2ab}$

$\frac{-(2a+b)}{(2a+b+2x)2x}=\frac{2a+b}{2ab}$

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

$4ax+2bx+4x^2=-2ab$

$4x^2+4ax+2bx+2ab=0$

$4x(x+a)+2b(x+a)=0$

$(x+a)(4x+2b)=0$

$x=-a,-\frac{b}{2}$

Hence, these are the roots of the given equation.