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Published byDelphia Shepherd Modified over 8 years ago

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Solving Rational Equations On to Section 2.8a

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Solving Rational Equations Rational Equation – an equation involving rational expressions or fractions…can always be written in the form: where f (x) and g (x) are polynomial functions with no common factors. The zeros of f (x) are the solutions of the equation…

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To solve an equation involving fractions: Find the LCD of all the terms in the equation. Clear the fractions by multiplying both sides of the equation by the LCD. Solve the resulting equation. Extraneous Solutions – solutions that are not solutions of the original equation; result from multiplying or dividing an equation by an expression containing variables…

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Guided Practice Solve The LCD is x !!! Multiply by x Subtract 4x Factor Zero Factor Property How do we support these answers numerically ???

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Guided Practice Solve The LCD is x – 4!!! How could we support these answers graphically ??? To solve this quadratic?

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Guided Practice Solve The LCD!!! First, factor the last denominator…

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Guided Practice Solve Factor!!! Confirm Numerically Support Graphically Extraneous Solution

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Guided Practice Solve LCD: Clear the fractions:

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Guided Practice Solve Algebraic solutions: Both solutions are extraneous!!! Substituting either solution into the original equation results in division by zero… The original equation has no solution!!!

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Practice Problems Solve Clear fractions: Extraneous

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Practice Problems Solve Clear fractions:

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Practice Problems Solve Clear fractions:

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Practice Problems Solve Clear fractions: Extraneous

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Practice Problems Solve Clear fractions: Solve graphically!

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