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