11.1 Simplifying Rational Expressions Goal: to simplify a rational expression Taken and modified from http://podcasts.shelbyed.k12.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.k12.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.k12.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.k12.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.k12.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.k12.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 ≠ 0 Thus x ≠ 9. x – 9 our domain is D:{ x | (-∞, 9) U (9, ∞) In 3x + 9 6x + 3 ≠ 0 Thus x ≠ -1/2. 6x+3 our domain is D:{ x | (-∞, -1/2) U (-1/2, ∞)} Taken and modified from http://podcasts.shelbyed.k12.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 3x + 9 x – 9 6x + 3 Taken and modified from http://podcasts.shelbyed.k12.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.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
The denominator can never = 0. *Remember The denominator can never = 0. Our constraints are: Taken and modified from http://podcasts.shelbyed.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
The denominator can never = 0. *Remember The denominator can never = 0. Our constraint is: Taken and modified from http://podcasts.shelbyed.k12.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.k12.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.k12.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.k12.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.k12.al.us/sclemons/files/2011/05/add-subtraction-rationals.ppt#1
Taken and modified from http://podcasts. shelbyed. k12. al
Taken and modified from http://podcasts. shelbyed. k12. al