Question

1/x-2 +2/x-1=6/x find out​

Answer 1

Answer:

$\frac{1}{x - 2} + \frac{2}{x - 1} = \frac{6}{x} \\ \frac{3x - 5}{(x - 1)(x - 2)} = \frac{6}{x} \\ {3x}^{2} - 5x = 6(x - 1)(x - 2) \\ {3x}^{2} - 5x = 6( {x}^{2} - 3x + 2) \\ - 3 {x}^{2} + 13x - 12 = 0 \\ 3 {x}^{2} - 13x + 12 = 0 \\ 3 {x }^{2} - 9x - 4x + 12 = 0 \\ 3x(x - 3) - 4(x - 3) = 0 \\ (3x - 4)(x - 3) = 0 \\ x = \frac{4}{3} \: \: \: \: x = 3$