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Solving Rational Equations

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

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Solving Rational Equations

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  1. Solving Rational Equations On to Section 2.8a

  2. 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…

  3. Solving Rational Equations 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…

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

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

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

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

  8. Guided Practice LCD: Solve Clear the fractions:

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

  10. Practice Problems Solve Clear fractions: Extraneous

  11. Practice Problems Solve Clear fractions:

  12. Practice Problems Solve Clear fractions:

  13. Practice Problems Solve Clear fractions: Extraneous

  14. Practice Problems Solve Clear fractions: Solve graphically!

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