Question

Solve $\frac{3}{x-1}-\frac{2}{x-2}=\frac{1}{x-3}$

Answer 1

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

$\frac{3x-6-2x+2}{x^2+2-3x}=\frac{1}{x-3}$

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

$\Rightarrow x^2-7x+12=x^2-3x+2$

$\Rightarrow 4x=10$

$\Rightarrow x=\frac{5}{2}$