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9.1 Multiplying and Dividing Rational Expressions. Complex fractions. Definition of a Rational Expression. In mathematics, a rational function is any function which can be written as the ratio of two polynomial functions. Since they are fractions. Simplify a Rational Expression. - PowerPoint PPT Presentation
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9.1 Multiplying and Dividing Rational Expressions
Complex fractions
Definition of a Rational Expression
In mathematics, a rational function is any function which can be written as the ratio of two polynomial functions.
Since they are fractions
Simplify a Rational Expression.
Divide the same expression from numerator and denominator
97
732
yy
yy
Since they are fractions
Simplify a Rational Expression.
Divide the same expression from numerator and denominator
97
732
yy
yy
9
3
97
7322
y
y
yy
yy
Since they are fractions
There are numbers that will not work in the Rational expression.
They are -7, 3 and -3. Why?
9
3
97
7322
y
y
yy
yy
Since they are fractions
Factor out the denominator.
Can you see why -7, 3 and -3 do not work as answers?
337
73
yyy
yy
Since they are fractions
Factor out the denominator.
-7, 3 and -3 do not work as answersbecause they make the denominator zero.
They are called Excluded Values.
337
73
yyy
yy
Simplify
Assume the denominator cannot equal zero.
baa
aba33
44
2
2
Simplify
Assume the denominator cannot equal zero.
Factor out a negative one to move things around
ba
ba
baa
aba
2
2
2
23
4
33
44
Simplify
Assume the denominator cannot equal zero.
ba
ba
ba
ba
baa
aba
2
2
2
2
2
2
3
4
3
4
33
44
Simplify
Assume the denominator cannot equal zero.
a
a
a
ba
ba
ba
ba
baa
aba
3
4
3
4
3
4
33
44
2
2
2
2
2
2
Multiply the fractions
Reduce to simplest form
3
5
7
12
Multiply the fractions
Reduce to simplest form.
Multiply straight across
21
60
3
5
7
12
Multiply the fractions
Reduce to simplest form
7
20
3
3
21
60
3
5
7
12
Multiply the fractions
Reduce to simplest form.
7
20
1
5
7
4
7
20
3
3
21
60
3
5
7
12
herehappenedWhat
Multiply the fractions
Reduce before multiply.
3
2
3 16
7
21
8
x
y
y
x
Multiply the fractions
Reduce before multiply.
yxxy
x
y
y
x
22
3
2
3
6
1
2
1
3
1
16
7
21
8
Multiply the fractions
Reduce before multiply.
23
24
15
24
12
5
ba
bc
b
ca
Multiply the fractions
Reduce before multiply.
2
3
2
2
23
24
3
2
3
2
1
15
24
12
5
b
ac
b
cac
ba
bc
b
ca
Multiply the fractions
Reduce before multiply.
34
1
1
32
2
kk
k
k
k
Multiply the fractions
Reduce before multiply.
13
1
1
3
34
1
1
3
2
2
2
kk
k
k
k
kk
k
k
k
Multiply the fractions
Reduce before multiply.
1
1
1
1
1
13
111
1
3
13
1
1
3
34
1
1
3
2
2
2
kk
kk
k
k
kk
k
k
k
kk
k
k
k
What is the difference of Division and Multiply of fractions?
Do you remember?
4
3
7
2
What is the difference of Division and Multiply of fractions?
When dividing you multiply by the inverse of the second fraction.
21
8
3
4
7
2
4
3
7
2
Divide the Rational Expressions
You can only Reduce when Multiplying
222
2
6
5
3
10
dc
px
dc
px
Divide the Rational Expressions
You can only Reduce when Multiplying
dxdx
px
dc
dc
px
dc
px
dc
px
41
2
1
2
5
6
3
10
6
5
3
10
22
2
2
222
2
Definition of Complex fraction
A fraction with fractions in the numerator or denominator.
7531
How to simplify a Complex fraction
Remember fractions are division statements.
15
7
5
7
3
1
7
5
3
1
7531
Simplify the Complex fraction
Remember fractions are division statements.
xyx
yxx
32
493
22
2
Simplify the Complex fraction
Remember fractions are division statements.
xy
x
yx
x
xyx
yxx
3249
32
49 3
22
2
3
22
2
Simplify the Complex fraction
322
23
22
2 32
493249 x
xy
yx
x
xy
x
yx
x
Simplify the Complex fraction
322
23
22
2 32
493249 x
xy
yx
x
xy
x
yx
x
3
2 231
2323 x
yx
yxyx
x
Simplify the Complex fraction
322
23
22
2 32
493249 x
xy
yx
x
xy
x
yx
x
3
2 231
2323 x
yx
yxyx
x
yxxxyx 23
11
23
1
Homework
Page 476 – 477
# 15,19, 23,
27, 31, 35,
37, 41
Homework
Page 476 – 477
# 16,20, 24,
28, 32, 36,
38, 40