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Published byFrank Sims Modified over 9 years ago

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Ch 8 - Rational & Radical Functions 8.5 – Solving Rational Equations

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A rational equation is an equation that contains one or more rational expressions. To solve a rational equation: 1.Find the LCM of the denominators. 2.Multiply EVERYTHING by the LCM (This clears the denominators) 3.Solve the equation. An extraneous solution is a solution of an equation derived from an original equation that is not a solution of the original equation.

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Solve the equation. The LCM is x, so multiply everything by x. x 2 -18=3x Now solve like normal x 2 -3x + 18 = 0 (x -3)(x+6)=0 x = 3, -6 Check 3 or -6 to make sure they are not undefined values of the original problem. If they are undefined values, then they are an extraneous solution, and we don’t include them in the answer.

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Solve each equation. The solution, x = 2 is an extraneous solution, so in this case, there are no solutions. All you need to write is no solution.

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Solve each equation. X = -4

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