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Solving Rational Equations

To solve an equation containing fractions, clear denominators by multiplying each term of the equation by the least common multiple, LCM, of the denominators. Then solve for the variable. Occasionally, a value of the variable that appears to be a solution will make one or more of the denominators zero. If that happens, the equation has no solution for that value of the variable.

Exercise:

Solve

Solution

The LCM is X - 5. Multiply each term by X - 5

3X = 5X - 25 - 5

3X = 5X - 30 SIMPLIFY:

-2X = -30

X = 15

15 checks as a solution.