Question

Solve: $\frac{1}{x-3}+\frac{2}{x-2}=\frac{8}{x},x\ne 0,2,3$

Answer 1

Given,

$\frac{1}{x-3}+\frac{2}{x-2}=\frac{8}{x}$

$\Rightarrow$ $\frac{x-2+2x-6}{(x-3)(x-2)}=\frac{8}{x}$

$\Rightarrow$ $x(3x-8)=8(x-3)(x-2)$

$\Rightarrow$ $3x^2-8x=8x^2-40x+48$

$\Rightarrow$ $5x^2-32x+48=0$

$\Rightarrow$ $(x-4)(x-\frac{12}{5})=0$

$\therefore x=4,\frac{12}{5}$