Question

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

Answer 1

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

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

$\Rightarrow$ $\frac{4x-8+3x+3}{2(x^2-2x+x-2)}=\frac{23}{5x}$

$\Rightarrow$ $\frac{7x-5}{2x^2-2x-4}=\frac{23}{5x}$

$\Rightarrow$ $35x^2-25x=46x^2-46x-92$

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

$\Rightarrow$ $11x^2-44x+23x-92=0$

$\Rightarrow$ $11x(x-4)+23(x-4)=0$

$\Rightarrow$ $(x-4)(11x+23)=0$

$\Rightarrow$ $x-4=0$ and $11x+23=0$

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