Question

Find the roots 6/x-2/x-1=1/x-2 ; x is not equal to 0,1,2​

Answer 1

Step-by-step explanation:

$\frac{6}{x} - \frac{2}{x - 1} = \frac{1}{x - 2}$

$\frac{6(x - 1) - 2x}{x(x - 1)} = \frac{1}{x - 2}$

$\frac{6x - 6 - 2x}{ {x}^{2} - x} = \frac{1}{x - 2}$

$\frac{4x - 6}{ {x}^{2} - x } = \frac{1}{x - 2}$

${x}^{2} - x = (x - 2)(4x - 6)$

${x}^{2} - x = 4 {x}^{2} - 6x - 8x + 12$

${x}^{2} - 4 {x}^{2} - x = - 14x + 12$

$- 3 {x}^{2} - x + 14x = 12$

$- 3 {x}^{2} + 13x - 12 = 0$

$- (3 {x}^{2} - 13x + 12) = 0$

$3 {x}^{2} - 13x + 12 = 0$

$3 {x}^{2} - (9 + 4)x + 12 = 0$

$3 {x}^{2} - 9x - 4x + 12 = 0$

$3x(x - 3) - 4(x - 3) = 0$

$(x - 3)(3x - 4) = 0$

Either, x-3=0 => x = 3

or, 3x -4=0 => 3x = 4 => x = 4/3

The values of x are 3 and 4/3.