Q) Solve the following quadratic equation by factorization method. $\frac{1}{\times - 2} + \frac {2}{\times - 1} = \frac{6}{\times}$

Let's find out the hidden quadratic equation: $\frac{1}{\times - 2}+\frac{2}{\times - 1} = \frac{6}{\times}$ ∴ $\frac{(\times - 1) + 2(\times - 2)}{(\times-2)(\times-1)} = \frac{6}{\times}$ ∴ $\frac{3\times - 5}{\times^{2} - 3\times + 2} = \frac{6}{\times}$ ∴ X (3 X - 5) = 6 (X2 - 3 X + 2) ∴ 3 X2 - 5X = 6X2 - 18X + 12 ∴ 3X2 -13 X + 12 = 0 ∴ 3 X2 - 9X - 4X + 12 = 0 ∴ 3 X(X - 3) - 4 (X - 3) = 0 ∴ (X - 3) (3 X - 4) = 0 ∴ therefore the roots are X = 3 and X = $\frac{4}{3}$ Please do press "Heart" button if you liked the solution.