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Linear Equations With Fractions: Clear Them Without Losing Terms

Updated September 26, 2026•Algebra & Equations

Clear fractions without changing the equation, solve step by step, and check your answer by substitution.

Fractions change the look, not the algebra

Fractions make an equation look complicated, but they do not change the basic rule: perform the same operation on both sides. A useful first move is often to clear denominators.

Clear the denominators in one clean move

Example: Solve x/3 + 2 = 7.

Subtract 2 from both sides: x/3 = 5.
Multiply both sides by 3: x = 15.

x = 15.

For several fractions, multiply the entire equation by the least common multiple of the denominators.

Example: Solve x/4 + x/6 = 5.

LCM(4,6) = 12 12(x/4 + x/6) = 12×5 3x + 2x = 60 5x = 60 x = 12

Distribute to every term

If you multiply an equation by 12, every term on both sides is multiplied by 12. Missing one term breaks the equality.

Watch negative signs

Example: (x−2)/5 = −3.

x − 2 = −15 x = −13

Substitute: (−13−2)/5 = −15/5 = −3.

The line where errors usually appear

Multiplying only a numerator instead of the full equation.
Using a denominator that does not clear all fractions.
Losing a minus sign after distributing.

Put the answer back into the original equation

Put your value of x back into the original equation. If both sides match, you have strong evidence the algebra is correct.

Try one yourself

Solve x/5 + 1 = 4. What is x?

Keep going

For another problem using related ideas, return to the Algebra & Equations page.