Algebra II For Dummies, 2nd Edition
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The problem with fractions in linear algebraic equations is that they aren't particularly easy to deal with. For example, they always require common denominators before you can add or subtract them.

The best way to deal with linear equations that involve variables tangled up with fractions is to get rid of the fractions. Your game plan is to multiply both sides of the equation by the least common denominator (also known as the least common multiple) of all the fractions in the equation.

For example, to solve

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your first step is to find the least common denominator for these fractions. In this case, the denominators are 5, 7, and 2, which means the least common denominator is 70. Now you multiply each term in the equation by the least common denominator:

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You then distribute the reduced numbers over each parenthesis, combine the like terms, and solve for x:

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Keep in mind that extraneous (false) solutions can occur when you alter the original format of an equation. When working with fractions and changing the form of an equation to a more easily solved form, always check your answer in the original equation. For this example, you just insert x = 3 into

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and get 1 + 2 = 3 or 3 = 3. This one checks.

About This Article

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About the book author:

Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

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