Question

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

Answer 1

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

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

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

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

$3x^2-9x-4x+12=3(x^2-3x+2)$

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

$-13x+12=-9x+6$

$13x-12=9x-6$

$13x-9x=12-6$

$4x=6$

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

$\therefore x=\frac{3}{2}$.