How do you simplify x / 3 - 2 / 3 = 1 / x?

May 11, 2018

color(green)(x = 3, -1

Explanation:

$\frac{x}{3} - \frac{2}{3} = \frac{1}{x}$

$\frac{x - 2}{3} = \frac{1}{x} \text{ taking 3 as L C M for L H S}$

$\left(x - 2\right) \cdot x = 3 \cdot 1 , \text{ cross multiplying}$

${x}^{2} - 2 x = 3 , \text{ removing bracket}$

${x}^{2} - 2 x - 3 = 0$

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

$x \left(x + 1\right) - 3 \left(x + 1\right) = 0$

$\left(x - 3\right) \cdot \left(x + 1\right) = 0$

color(green)(x = 3, -1