Equations with fractions on both sides

If an equation has fractions on both sides, multiply both sides by the lowest common multiple (LCM) of the denominators.

Example

Solve this equation:

\frac {(x - 3)} {2} = \frac {(x - 2)} {3}

Solution

One side is divided by 2. The other side is divided by 3. The lowest common multiple of 2 and 3 is 6, so multiply both sides by 6.

\frac {(x - 3)} {2} \times 6 = \frac {(x - 2)} {3} \times 6

3(x - 3) = 2(x - 2)

Expand the brackets:

3x - 9 = 2x - 4

Take 2x from both sides:

x - 9 = - 4

Add 9 to both sides:

x = 5

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