Question

Solve for x
$\frac{2}{x+1}+\frac{3}{2(x-2)}=\frac{23}{5x},x\ne 0,-1,2$

Answer 1

$\frac{2}{x+1}+\frac{3}{2(x-2)}=\frac{23}{5x},x\ne 0,-1,2$

$\Rightarrow \frac{4(x-2)+3(1+x)}{2(1+x)(x-2)}=\frac{23}{5x}$

$\Rightarrow 20x^2-40x+15x+15x^2=46x^2-46x-92$

$\Rightarrow 11x^2-21x-92=0$

$x=\frac{21\pm \sqrt{441+4\left(92\right)\left(11\right)}}{2\left(11\right)}$

$x=\frac{21\pm \sqrt{4}489}{2\left(11\right)}$

$x=\frac{21\pm 67}{2\left(11\right)}$

$x=4,\frac{-23}{11}$