Lesson 31 Section 6.1Rational Expressions and FunctionsA Rational Expression is a polynomial divided by a non-zero polynomial.The following are examples of rational expressions.852 ,13 ,59 ,2 ,43222yyyrrrxxwA Rational Function is a function where f (x) is represented by a rational expression.1) Evaluate the following rational function for the given values.513)(2xxxxG for x = 0, -2, 3, and 5Procedure for Simplifying Rational Expression:I. Factor each denominator and numerator.II. You may cancel the same factor found in a numerator and a denominator, since they equal a factor of 1. You may also cancel a factor in a numerator that is opposite of a factor in the denominator and that quotient equals a factor of -1.III. The simplified rational expression is the factors that remain.Caution: Cancel only Factors, never Terms!!!!Simplify each expression.2)30253))52)(3()3)(2(xxxx14)baba332645)aa6123 6)yyyy636227)yyy12420428)xxx969422Remember: Opposite reduce to -11331 xx1baab9))2()3)(2(xxxx2Procedure for Multiplying or Dividing Rational Expressions and writing the product orquotient in simplified form:I. Factor each numerator and denominator.II. Cancel any factor the same in the numerator and denominator or opposite factors. III. Multiply across and leave in factored form.IV. With division, multiply by the reciprocal of the divisor.Multiply or divide. Write answers in simplified form.10)baba6831632211)mmmm101268452-12)6561552122-aaaaa13)222123344xxyyxyx
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