Question

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

Answer 1

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

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

$(3x-4)(x-3)=3(x-1)(x-2)$

$3x(x-3)-4(x-3)=3\left[x\right(x-2)-1(x-2\left)\right]$

$3x^2-9x-4x+12=3[x^2-2x-x+2]$

$3x^2-13x+12=3x^2-9x+6$

$4x=6$

$x=\frac{6}{4}=\frac{3}{2}$