Equations with Fractions

≈ 30 min

Fractions disappear if you multiply the whole equation by the lowest common denominator (LCD).

Worked example 1. Solve $\dfrac{x}{3} = 7$ . Multiply both sides by 3: $x = 21$ .

Worked example 2. Solve $\dfrac{x+1}{2} = \dfrac{x-2}{3}$ .

The LCD of 2 and 3 is 6 — multiply both sides by 6:

3(x + 1) = 2(x - 2)

3x + 3 = 2x - 4

x = -7

Check: LHS $= \frac{-7+1}{2} = -3$ ; RHS $= \frac{-7-2}{3} = -3$ ✓

Solve for $x$ : $\dfrac{x}{3} = 7$

Solve for $x$ : $\dfrac{2x}{5} = 6$

Solve and answer in the form x=…: $\dfrac{x+1}{2} = \dfrac{x-2}{3}$

To clear all fractions from $\dfrac{x}{4} + \dfrac{x}{6} = 5$ , multiply every term by…