Solving Rational Equations On to Section 2 8

Solving Rational Equations On to Section 2. 8 a

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…

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…

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

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

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

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

Guided Practice Solve Clear the fractions: LCD:

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!!!

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!