Question

1/(x-1)+2/(x-2)= 3/(x-3)

Answer 1

$\mathfrak{\huge{Answer:}}$

$\frac{1}{(x - 1)} + \frac{2}{(x - 2)} = \frac{3}{(x - 3)} \\ \\ = > \frac{1(x - 2) + 2(x - 1)}{(x - 1)(x - 2)} = \frac{3}{(x - 3)} \\ \\ = > \frac{x - 2 + 2x - 2}{ {x}^{2} - 2x - x + 2 } = \frac{3}{(x - 3)} \\ \\ = > (x - 3)(3x - 4) = 3( {x }^{2} - 2x - x + 2) \\ \\ = > 3 {x}^{2} - 4x - 9x + 12 = 3 {x}^{2} - 6x - 3x + 6 \\ \\ = > 12 - 6 = - 9x + 9x + 4x \\ \\ = > 6 = 4x \\ \\ = > \frac{6}{4} = x \\ \\ = \geqslant \frac{3}{2} = x$