Question

If $2+\frac{2x-3}{2x+3}=\frac{3x+4}{x+2}$ then the value of $x$ is :

Answer 1

$2+\frac{2x-3}{2x+3}=\frac{3x+4}{x+2}$

$\Rightarrow 1+\frac{2x-3}{2x+3}=\frac{3x+4}{x+2}-1$

$\Rightarrow \frac{2x+3+2x-3}{2x+3}=\frac{3x+4-x-2}{x+2}$

$\Rightarrow \frac{4x}{2x+3}=\frac{2x+2}{x+2}$

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

$\Rightarrow 2x(x+2)=(x+1)(2x+3)$

$\Rightarrow {2x}^2+4x={2x}^2+5x+3$

$\Rightarrow 5x-4x=-3$

$\Rightarrow x=-3$