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Pre-Calculus Notes §3.7 Rational Functions
Excluded Number: A number that must be excluded from the domain of a function because it makes the denominator zero.
Example1: State the excluded values. excluded values: ___________________
To simplify rational expressions: (1) (2) Factor numerator and denominator Cancel common factors
Example2: Simplify and state excluded values. a) excluded values: ___________________ b) simplified: ______________________ X = -1 and -5
To multiply or divide rational expressions: (1) (2) (3) (4) Change division to multiplication by reciprocal ( if necessary) Factor numerator and denominator Cancel common factors Multiply across
Example3: Simplify and state excluded values. a) excluded values: ___________________ b) simplified: ______________________ Note: another excluded value: x = 2, x = 2
Dividing Rational Expressions Use the following steps to divide rational expressions. 1.Take the reciprocal of the rational expression following the division.
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Operations on Rational Expressions. Rational expressions are fractions in which the numerator and denominator are polynomials and the denominator does.
Warm up # (-24) =4.) 2.5(-26) = 2-7(-8)(-3) = 5.) -5(9)(-2) = 3.
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MULTIPLY and DIVIDE RATIONAL NUMBERS. MULTPILYING MIXED NUMBERS 1)Change all Mixed numbers to improper fractions 2)Simplify A) Up and Down B) Diagonally.
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