Rational Expressions

1. SIMPLIFYING RATIONAL
EXPRESSIONS

2. RATIONAL EXPRESSIONS
Q
P
Rational expressions can be written in the
form where P and Q are both polynomials
and Q  0.
Examples of Rational
Expressions
54
423 2


x
xx
22
432
34
yxyx
yx


4
3 2
x

3. Simplify the following expression.



xx
x
5
357
2



)5(
)5(7
xx
x
x
7
Example

4. Simplify the following expression.



20
43
2
2
xx
xx



)4)(5(
)1)(4(
xx
xx
5
1


x
x
Example

5. Simplify the following expression.



7
7
y
y



7
)7(1
y
y
1
Example

6. MULTIPLYING AND DIVIDING
RATIONAL EXPRESSIONS

7. Multiply the following rational expressions.





mnm
m
nm
nm
2
2
)(
)()(
))((
nmmnm
mnmnm


nm
nm



Example

8. FROM MODULE 3 LESSON 3 ASSIGNMENT
𝑥 + 4
3(𝑥 + 2)
∙
3
2(𝑥 + 5)
3(𝑥 + 4)
6(𝑥 + 2)(𝑥 + 5)
(𝑥 + 4)
2(𝑥 + 2)(𝑥 + 5)
- Original Problem
- Multiply the top
together and multiply
the bottom together
- simply what you can

9. DIVIDING RATIONAL EXPRESSIONS
Divide the following rational expression.




25
155
5
)3( 2
xx




155
25
5
)3( 2
x
x



)3(55
55)3)(3(
x
xx
3x
Example

10. FROM MODULE 3 LESSON 3 ASSIGNMENT
(𝑥 − 9)
6𝑥3 − 54𝑥2
÷
1
𝑥 − 14
1. Original problem
2. FACTOR
3. Multiply by the ”flip” of
the bottom
4. multiply across the top
and across the bottom
5. simplify what you can
(𝑥 − 9)
6𝑥2(𝑥 − 9)
÷
1
𝑥 − 14
(𝑥 − 9)
6𝑥2(𝑥 − 9)
∙
(𝑥 − 14)
1
(𝑥 − 9)(𝑥 − 14)
6𝑥2(𝑥 − 9)
𝑥 − 14
6𝑥2