Question

$\frac{1}{x - 2} + \frac{2}{x - 1} = \frac{6}{x}$
where x is not equal to 0
answer : 3 or 4/3​

Answer 1

Explanation:-

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

Taking LCM

$\implies \frac{x - 1 + 2x - 4}{(x - 2)(x - 1)} = \frac{6}{x} \\ \\ \implies \: \frac{3x - 5}{(x - 2)(x - 1)} = \frac{6}{x} \\ \\ \implies \: 3 {x}^{2} - 5x = 6( {x}^{2} - x - 2x \: + 2) \\ \\ \implies \: 3 {x}^{2} - 5x = 6 {x}^{2} - 18x + 12 \\ \\ \implies \: 3 {x}^{2} - 13x + 12 = 0 \\ \\ \implies \: 3 {x}^{2} - (9 + 4)x + 12 = 0 \\ \\ \implies \: 3 {x}^{2} - 9x - 4x + 12 = 0 \\ \\ \implies \: 3x(x - 3) - 4(x - 3) = 0 \\ \\ \implies \: (x - 3)(3x - 4) = 0$

(1.)x = 3

(2.)x = 4/3

hope it helps you.