Question

Solve for $x$ : $\frac{x}{2x+1}+\frac{2x+1}{x}=1$

Answer 1

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

$\Rightarrow \frac{x^2+{(2x+1)}^2}{2x^2+x}=1$

$\Rightarrow x^2+4x^2+1+4x=2x^2+x$

$\Rightarrow 5x^2+1+4x-2x^2-x=0$

$\Rightarrow 3x^2+3x+1=0$

$\Rightarrow x=\frac{-3\pm \sqrt{3^2-4\times 3\times 1}}{2\times 1}$

$\therefore x=\frac{-3\pm \sqrt{9-12}}{2}$

$\therefore x=\frac{-3\pm i\sqrt{3}}{2}$