How to Solve an Equation by Clearing Fractions First

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Equations containing variables are an important part of algebra and upper-level math, and sometimes you will have to clear an equation of fractions to solve it. Fortunately, the process is relatively simple, and it involves conducting the same mathematical operations on both sides of the equal sign.

  • Find a least common multiple for all of the denominators in the equation. The least common multiple is the smallest number that all of the denominators will divide into, with no remainder. If your equation is (x/2) - (5x/6) = (1/9), the least common multiple among 2, 6 and 9 is 18.

  • Multiply every term in the fraction by the least common multiple. This yields (18x/2) - (5*18x/6)= (18/9).

  • Simplify the terms in Step 2 to obtain 9x - 15x = 2.

  • Combine the x-terms. This gives -6x = 2.

  • Isolate x to obtain x =-2/6, or -1/3.

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