4Section 12.4 “Simplify Rational Expressions” A RATIONAL EXPRESSION is an expression that can be written as a ratio (fraction) of two polynomials where the denominator is not 0.
5Simplify Rational Expressions To simplify a rational expression, you can factor the numerator and denominator and then divide out any common factors.A rational expression is in SIMPLEST FORM if the numerator and denominator have no factors in common other than 1.
6Simplify the rational expression, if possible. FactorFactorRecognizeoppositesMultiply by -1Rewrite (z-5) as -(z+5)
7Section 12.5 “Multiply and Divide Rational Expressions” Multiplying and dividing rational expressions is similar to multiplying and dividing fractions.Be sure to simplify your answer. Look to cancel like terms when multiplying or dividing.Multiply by reciprocal,then look to cancel terms.
8Find the product or quotient. EXAMPLE 1Find the product or quotient.Multiply by reciprocal
9Find the product. EXAMPLE 2 Multiply numerator and denominator. Factor and look for common factors to cancel.
10Find the quotient. Try it out. EXAMPLE 2Find the quotient. Try it out.Multiply by reciprocalMultiply numeratorand denominator.Factor and look for common factors to cancel.
11Find the product. EXAMPLE 3 Multiply numerator and denominator. Factor and look for common factors to cancel.
12Section 12.6 “Add and Subtract Rational Expressions” Adding and subtracting rational expressions is similar to adding and subtracting fractions.Be sure to simplify your answer.Denominator must be COMMON!!!
13Find the sum or difference. EXAMPLE 5Find the sum or difference.LCD = (x+5)(x – 2)(x + 4)
14Section 12.7 “Solve Rational Equations” A RATIONAL EQUATION is an equation that contains one or more rational expressions.One method for solving a rational equation is to use the cross products property. (You can use this method when both sides of the equation are single rational expressions).
15Solve the equation. Check your solution. Check for extraneous solutionsCross multiplyy = 5y = -3