Question

Solve of $x$ :
$2\left(\frac{2x-1}{x+3}\right)-3\left(\frac{x+3}{2x-1}\right)=5$

Answer 1

Let $\frac{2x-1}{x+3}=y$

$\Rightarrow 2y-\frac{3}{y}=5$

$\Rightarrow 2y^2-5y-3=0$

$\Rightarrow 2y^2-6y+y-3=0$

$\Rightarrow 2y(y-3)+(y-3)=0$

$\Rightarrow (2y+1)(y-3)=0$

$\Rightarrow y=3$ or $y=-\frac{1}{2}$

$\Rightarrow 2x-1=3x+9$ or $2x-1=\frac{-x}{2}-\frac{3}{2}$

$\Rightarrow 4x-2=-x-3$

$\Rightarrow 5x=-1$

$\Rightarrow x=\frac{-1}{5}$

$\Rightarrow x=-10$.