Transcript Simplifying Rational Expressions

Warm – Up2/12/07
Simplify the following
3
1
1)
15
5
2
3x
2)
15 x
2
x
5
2
3
x
y
3)
3
15 xy
x
5y
Agenda
 Notes
on Rational
Expressions
 Questions
 Homework
Assignment
Tues: More
Simplifying Rational
Expressions
WEB: Multiply &
Divide Rational
Expressions
Thur: Review
Rational
Expressions
Friday 2/16
Quiz: 11.4 – 11.5
Simplifying Rational
Expressions
Let’s start with what’s a rational number
– a number that can be written as the
quotient of two integers.
HUH?
What does that mean?
Here are a few examples of Rational
Numbers: ½, ⅓, ¼, ¾
You mean they’re just fractions?
YEP – that’s it - Rationals are fractions!!
Sooooo
What does that have to do with RATIONAL
EXPRESSIONS?
Remember what an expression looks like?
3
2
Here’s one: 3 x  9 x  x  7
So if Rationals look like fractions and
Expressions have terms added and
subtracted, then a Rational Expression is….
…..a Fraction with terms that
have variables and numbers
Here are a few examples:
7
x3
5x
2
x  16
2x 1
2
x 1
Let’s simplify a few…
Recall how to
simplify the
fractions:
Use the same
steps for
Rational
Expressions
12 12  1 1


36 12  3 3
This x is
a term
NOT a
Only cancel Factor
common
FACTORS
5 x  5 5( x  1) ( x  1)


5x
5x
x
Only cancel
common
FACTORS
Simplify
2
2 x x
2x
2x


2
x  5 x x( x  5) x  5
Only cancel
common
FACTORS
Let’s talk about plain ole
fractions again….
What happens if there is a zero
in the denominator of a fraction?
7
0
We say this is
‘undefined’
Likewise Rational Expressions
with zero in the denominator is
also ‘undefined’
We’ll always determine what
would make the denominator
zero and exclude those values
for the variable.
7
x3
5x
2
x  16
2x 1
2
x 1
Undefined Expressions
One way to determine what will make
the denominator zero is to set it
equal to zero.
2x 1
2
x 1
Set the denominator
equal to zero and
solve – this is what
we do NOT want!!!
x 1  0
2
x 1
x  1
2
So x can be
anything except
+1 and -1!!!
Let’s look at the we just worked.
For what value of the variable is
the expression undefined?
15 x  5 5(3 x  1) (3 x  1)


5x
5x
x
2
2x  x
2x
2x


2
x  5 x x( x  5) x  5
x=0 would
make the
expression
undefined
x=-5 would
make the
expression
undefined
Homework
 p.667:
1-5 all; 9-18 all