Question

Factorise 1/x-1+2/x-2=3/x-3

Answer 1

Answer:

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

Step-by-step explanation:

$\frac{1}{x - 1} + \frac{2}{x - 2} = \frac{3}{x - 3} \\ \frac{1(x - 2) + 2(x - 1)}{(x - 1)(x - 2)} = \frac{3}{x - 3} \\ \frac{x - 2 + 2x - 2}{x(x - 2) - 1(x - 2)} = \frac{3}{x - 3} \\ \frac{x + 2x - 2 - 2}{ {x}^{2} - 2x - x + 2 } = \frac{3}{x - 3} \\ \frac{3x - 4}{ {x}^{2} - 3x + 2} = \frac{3}{x - 3} \\ cross \: multiply\\ 3( {x}^{2} - 3x + 2) = (x - 3)(3x - 4) \\ 3 {x}^{2} - 9x + 6 = x(3x - 4) - 3(3x - 4) \\ 3 {x}^{2} - 9x + 6 = 3 {x}^{2} - 4x - 9x + 12 \\ 3 {x}^{2} - 3 {x}^{2} - 9x + 9x + 4x + 6 - 12 = 0 \\ 4x - 6 = 0 \\ 4x = 6 \\ x = \frac{6 }{4} = \frac{3}{2}$