Question

Solve 6 upon x - 2upon x-1 =1upon x-2 x is not equal to zero one and two

Answer 1

Answer:

$x = \frac{4}{3} and \: x = 3$

Step-by-step explanation:

$\frac{6}{x} - \frac{2}{x - 1} = \frac{1}{x - 2} \\ \frac{6x - 6 - 2x}{ {x}^{2} - x} = \frac{1}{x - 2} \\ \frac{4x - 6}{ {x}^{2} - x} = \frac{1}{?x - 2} \\ 4 {x}^{2} - 8x - 6x + 12 = {x}^{2} - x \\ 4 {x}^{2} - 14x + 12 - {x}^{2} + x = 0 \\ 3 {x}^{2} - 13x + 12 = 0 \\ 3 {x}^{2} - 9x - 4x + 12 = 0 \\ 3x(x - 3) - 4(x - 3) = 0 \\(3x - 4)(x - 3) = 0 \\ take \: 3x - 4 = 0 \\ x = \frac{4}{3} and \: take \: x - 3 = 0 \\ x = 3$