Warm-up

1
Warm-up

• Given these solutions below write the equation
  of the polynomial
• 1. -1, 2, ½)

2
Rational Equations

• Section 2-6

3
Objectives

• I can simplify rational expressions
• I can find Domain Restrictions
• I can solve rational equations with one variable

4
Simplifying Rational Expressions

• Try and reduce numerator over denominator
• You will factor all numerators and denominators,
  then
• Reduce or cancel like terms

5
Domain 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)

6
EXAMPLE 1
Simplify a rational expression
SOLUTION
Factor numerator and denominator.
Divide out common factor.
Simplified form
7
for Examples 1 and 2
GUIDED PRACTICE
5.
SOLUTION
Factor numerator and denominator.
Divide out common factor.
Simplified form
8
for Examples 1 and 2
GUIDED PRACTICE
6.
SOLUTION
Factor numerator and denominator.
Divide out common factor.
Simplified form
9
Adding Subtracting Rational Expressions

• MUST have a COMMON DENOMINATOR
• You will factor all denominators, then find the
  Common Denominator
• Reduce or cancel like terms

10
Basic 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)
12
2
2(x-5)
2(x-5) - 1(x-7)
2
1
x - 7
1
13
Solving 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

14
Cross Multiplication Method
15
Cross Multiplication Ex2
16
Set 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
17
Problem Continued
MUST CHECK ANSWERS x 2 does not work
18
Extraneous 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

19
Homework

• Worksheet 5-1