Title: Warm-up
1Warm-up
- Given these solutions below write the equation
of the polynomial - 1. -1, 2, ½)
2Rational Equations
3Objectives
- I can simplify rational expressions
- I can find Domain Restrictions
- I can solve rational equations with one variable
4Simplifying Rational Expressions
- Try and reduce numerator over denominator
- You will factor all numerators and denominators,
then - Reduce or cancel like terms
5Domain of Rational Functions
- The domain of any rational function is all real
numbers except where the following happens - No x-value that makes denominator zero
- No x-value that would be a discontinuity (hole)
6EXAMPLE 1
Simplify a rational expression
SOLUTION
Factor numerator and denominator.
Divide out common factor.
Simplified form
7for Examples 1 and 2
GUIDED PRACTICE
5.
SOLUTION
Factor numerator and denominator.
Divide out common factor.
Simplified form
8for Examples 1 and 2
GUIDED PRACTICE
6.
SOLUTION
Factor numerator and denominator.
Divide out common factor.
Simplified form
9Adding Subtracting Rational Expressions
- MUST have a COMMON DENOMINATOR
- You will factor all denominators, then find the
Common Denominator - Reduce or cancel like terms
10Basic Fraction
x2
4
6
4 3
x2
x3
3
6
6
x3
11(x2)
x(x2)
x(x2) - 2(x3)
(x2)
(x3)
2(x3)
(x3)
122
2(x-5)
2(x-5) - 1(x-7)
2
1
x - 7
1
13Solving Rational Equations
- Two basic methods
- 1. Set equation equal to ZERO and then get
Common Denominator - 2. Two ratios equal means you can Cross Multiply
to solve them
14Cross Multiplication Method
15Cross Multiplication Ex2
16Set Equation to ZERO
2
2(x1)
2
5x(x-2)
2(x1) 5x(x-2) - 6
(x-2)
6(x-2)
(x-2)
6
6
Next Slide
6
17Problem Continued
MUST CHECK ANSWERS x 2 does not work
18Extraneous Solutions
- Extraneous solutions are those that do not work
when you plug them back into the original
equation. - Usually they dont work because they make the
Denominator zero
19Homework