11 1 Simplifying Rational Expressions Goal to simplify

Simplifying Rational Expressions • A “rational expression” is the quotient of two polynomials. (division)

Simplifying Rational Expressions Again, we can not cancel a 3 because there is addition/subtraction

How to get a rational expression in simplest form… • Factor the numerator completely

How to write the domain with constrains… • The constrain(s) of a rational expression

Difference between a factor and an addend • A factor is in between a

Factor *Remember The denominator can never = 0. Our constraint is: Taken and modified

*Remember The denominator can never = 0. Our constraints are: Taken and modified from

*Remember The denominator can never = 0. Our constraint is: Taken and modified from

*Do not forget to include your constrains: Taken and modified from http: //podcasts. shelbyed.

Taken and modified from http: //podcasts. shelbyed. k 12. al. us/sclemons/files/2011/05/add-subtraction-rationals. ppt#1

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11. 1 Simplifying Rational Expressions • Goal: to simplify a rational expression Taken and modified from http: //podcasts. shelbyed. k 12. al. us/sclemons/files/2011/05/add-subtraction-rationals. ppt#1

Simplifying Rational Expressions • A “rational expression” is the quotient of two polynomials. (division) Taken and modified from http: //podcasts. shelbyed. k 12. al. us/sclemons/files/2011/05/add-subtraction-rationals. ppt#1

Simplifying Rational Expressions • A “rational expression” is the quotient of two polynomials. (division) • A rational expression is in simplest form when the numerator and denominator have no common factors (other than 1) Taken and modified from http: //podcasts. shelbyed. k 12. al. us/sclemons/files/2011/05/add-subtraction-rationals. ppt#1

Simplifying Rational Expressions • A “rational expression” is the quotient of two polynomials. (division) • A rational expression is in simplest Form when the numerator and denominator have no common factors (other than 1) We can not cancel the 3 because there is addition/subtraction included. We can only cancel if we have multiplication. Taken and modified from http: //podcasts. shelbyed. k 12. al. us/sclemons/files/2011/05/add-subtraction-rationals. ppt#1

Simplifying Rational Expressions Again, we can not cancel a 3 because there is addition/subtraction included. We can only cancel if we have multiplication. Taken and modified from http: //podcasts. shelbyed. k 12. al. us/sclemons/files/2011/05/add-subtraction-rationals. ppt#1

How to get a rational expression in simplest form… • Factor the numerator completely (factor out a common factor, difference of 2 squares, bottoms up) • Factor the denominator completely (factor out a common factor, difference of 2 squares, bottoms up) • Cancel out any common factors (not addends) Taken and modified from http: //podcasts. shelbyed. k 12. al. us/sclemons/files/2011/05/add-subtraction-rationals. ppt#1

How to write the domain with constrains… • The constrain(s) of a rational expression is a number(s) that cannot be included in the domain because it will make the denominator equal to zero. In x + 3 x– 9 In 3 x + 9 6 x+3 x – 9 ≠ 0 Thus x ≠ 9. our domain is D: { x | (-∞, 9) U (9, ∞) 6 x + 3 ≠ 0 Thus x ≠ -1/2. our domain is D: { x | (-∞, -1/2) U (-1/2, ∞)} Taken and modified from http: //podcasts. shelbyed. k 12. al. us/sclemons/files/2011/05/add-subtraction-rationals. ppt#1

Difference between a factor and an addend • A factor is in between a multiplication sign • An addend is in between an addition or subtraction sign Example: x+3 3 x + 9 x– 9 6 x + 3 Taken and modified from http: //podcasts. shelbyed. k 12. al. us/sclemons/files/2011/05/add-subtraction-rationals. ppt#1

Factor *Remember The denominator can never = 0. Our constraint is: Taken and modified from http: //podcasts. shelbyed. k 12. al. us/sclemons/files/2011/05/add-subtraction-rationals. ppt#1

*Remember The denominator can never = 0. Our constraints are: Taken and modified from http: //podcasts. shelbyed. k 12. al. us/sclemons/files/2011/05/add-subtraction-rationals. ppt#1

*Remember The denominator can never = 0. Our constraint is: Taken and modified from http: //podcasts. shelbyed. k 12. al. us/sclemons/files/2011/05/add-subtraction-rationals. ppt#1

*Do not forget to include your constrains: Taken and modified from http: //podcasts. shelbyed. k 12. al. us/sclemons/files/2011/05/add-subtraction-rationals. ppt#1

Taken and modified from http: //podcasts. shelbyed. k 12. al. us/sclemons/files/2011/05/add-subtraction-rationals. ppt#1

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