7.1: simplifying rational expressions march 31, 2009
TRANSCRIPT
7.1: Simplifying Rational Expressions
March 31, 2009
Topics for review
• Multiplying monomials• Graphing• Factoring
Multiplying monomials
Graphing
Graphing
factoring
• Find ac and b• Find two numbers that add to equal b and
multiply to equal ac• Split b in half, using these numbers• Factor by grouping
Factoring
5x2-8x-4=0
Factoring
9x2+4x-5=0
This week
• Monday: review• Tuesday: lecture (7.1)• Wednesday: work day• Thursday: lecture (7.2)• Friday: quiz (7.1 only)/work day
Objectives
• Simplify rational expressions• Identify rational functions• Simplify rational functions• Graph rational functions
Standards Addressed
• Algebraic Relationships– Analyze the nature of change of each variable in a
non-linear relationship as suggested by a table of values, a graph or a formula
– Evaluate and make a table for two-variable formulas and match a graph or table of values to its formula
• Calculations and Estimations– Apply the associative, commutative, and distributive
properties to simplify computations with real numbers
What does rational mean?
• Rational comes from the word ratio, which means
fraction!• Rational expressions are expressions that
can be written as fractions.
Precluding division by zero
Any value divided by zero is undefined.
Find the value for x for which the following rational expressions are undefined.
1
103
x
x
21
2
10
x
A few more
1021
57
x
x
2
53 x
Evaluating a rational expression
To evaluate means to solve for a given value of x.
Evaluate the following rational expression for x = 3.
52
3
xx
A few more
• Evaluate for x= -2.
23
62
x
xx
x
2
36
Simplifying a rational expression
• Monomial: one term• Simplifying monomials:
Cancel out common factors
310
125
8
6
yx
yx
A couple more
17312
15102
24
56
zyx
zyx
126
64
60
36
ba
ba
Simplying non-monomial rational expressions1) Factor the numerator and the
denominator, using the GCF or the ac method (sometimes factoring out -1 can be helpful)
2) Cancel out common factors
An example
Try this one:
44
22
2
xx
xx
Try another
24
42
x
x
And another…
32
622
2
xx
xx
Identifying a rational function
• A rational function must be able to be written as a ratio, even if the denominator is simply 1.
• There cannot be any square roots.
Simplifying a rational function
1) Examine the denominator. Determine what value of x will make the denominator equal zero. Write x ≠ (that number).
2) Then simplify as before.
3) The answer will be the simplify version, plus part 1.
Try it
• Try this one.
1
12)(
2
x
xxxf
Try another
x
xxxf
5
105)(
2
Graphing a rational function
1) Simplify the function.
2) Note what x cannot equal (≠).
3) Plug that value in and determine the y value. Mark an open circle at the ordered pair (x, y) that you have just found. This is called a hole.
4) Graph normally.
Try it
Remember this one?
1
12)(
2
x
xxxf
Try another
What about this one?
x
xxxf
5
105)(
2
Your assignment
• Pages 489-490
2-36 even
40-66 even