40Solving rational equation

Solve $\displaystyle \dfrac{1}{x} + \dfrac{1}{x + 2} = \dfrac{4}{3}$.

Clearing the fractions turns the equation into 4x² + 2x − 6 = 0, which factors to (2x+3)(x−1) = 0, giving x = 1 or x = −3/2. Checking x = 1: 1/1 + 1/3 = 4/3 ✓, and neither value makes a denominator zero.