10/24/11 Section 6.1 and 6.2
•  Find the domain of a rational function.
•  Evaluate a rational function.
•  Simplify rational expressions.
•  Multiply rational expressions and simplify.
•  Divide rational expressions and simplify
Rational expressions
•  If we divide two polynomials u and v we obtain a rational
expression:
•  The domain of this expression is the set of all real
numbers for which v ≠ 0.
1 10/24/11 Rational functions
•  If we have two polynomial functions u(x) and v(x), the
function
is a rational function whose domain is the set of all real
numbers where v(x) ≠ 0.
Find the domains
2 10/24/11 Find the domains
Evaluate
3 10/24/11 1.  Yes
2.  No
3.  I’m not sure
Simplifying the rational functions
•  If the numerator and denominator of a rational function
(expression) have common factors we can cancel them
after we record what the domain must be.
4 10/24/11 What is the domain of
1.  All real numbers r
2.  All real numbers r such that
r≠2 and r≠3
3.  All real numbers r such that
r≠2
4.  I have no idea
u w u z uz
÷ = ⋅ =
v z v w vw
In order to determine the domain, we want
to fine the values such that :
1.  v≠0, z≠0
€
2.  v≠0, w≠0
3.  v≠0, z≠0, w≠0
5 10/24/11 Examples: Simplify
Section 6.3.
•  Add rational expressions.
•  Subtract rational expressions
6 10/24/11 Operations on rational functions
•  Just like you would with fractions!
7 10/24/11 More: Add and simplify
8 10/24/11 •
x
2x
2x
Describe and correct the errors
•
9 10/24/11 Section 6.5: Dividing polynomials
•  Divide polynomials by monomials and simplify.
•  Use long division to divide polynomials by polynomials.
Dividing polynomials
•  Find
10 10/24/11 Dividing polynomials
•  Solve
•  Let’s do 5724÷3 first, or rather in parallel.
11 10/24/11 Dividing polynomials
Dividing polynomials
12 10/24/11 Dividing polynomials
13