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Procedure for Solving a Rational Equation
To solve an equation containing rational expressions, follow this five-step procedure:
Step 1. Identify restricted values. Determine any values of the variable that would cause any denominator in the equation to equal . Step 2. Determine the LCD. Find the least common denominator of all the rational expressions present in the equation. Step 3. Clear the fractions. Multiply both sides of the equation by the LCD to eliminate the denominators, resulting in a simpler, fraction-free equation. Step 4. Solve the new equation. Apply standard algebraic techniques to solve the resulting equation for the variable. Step 5. Check for extraneous solutions. Compare the algebraic solutions against the restricted values from Step 1. Discard any solution that makes a denominator , and verify any remaining valid solutions by substituting them back into the original equation.
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Intermediate Algebra @ OpenStax
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Procedure for Solving a Rational Equation