Solving Rational Equations On to Section 2.8a. Solving Rational Equations Rational Equation – an equation involving rational expressions or fractions…can.

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Presentation transcript:

Solving Rational Equations On to Section 2.8a

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…

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…

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

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

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

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

Guided Practice Solve LCD: Clear the fractions:

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!!!

Practice Problems Solve Clear fractions: Extraneous

Practice Problems Solve Clear fractions:

Practice Problems Solve Clear fractions:

Practice Problems Solve Clear fractions: Extraneous

Practice Problems Solve Clear fractions: Solve graphically!