Chapter 2

2.1 – Simplifying Rational Expressions
2.2 – Multiplying and Dividing Rational Expressi
ons
2.3 – Adding and Subtracting Rational Expressi
ons with the Same Denominator and Least Common
Denominators
2.4 – Adding and Subtracting Rational Expressio
ns with Different Denominators
2.5 – Simplifying Complex Fractions
Chapter Sections

Simplifying
Rational
Expressions

Simplifying
a rational expression means writing it in
lowest terms or simplest form.
To do this, we need to use the
Fundamental Principle of Rational Expressions
If
P
,
Q
, and
R
are polynomials, and
Q
and
R
are not 0,
Q
P
QR
PR
Simplifying Rational Expressions

Simplifying a Rational Expression
1)
Completely factor the numerator and
denominator.
2)
Apply the Fundamental Principle of Rational
Expressions to eliminate common factors in
the numerator and denominator.
Warning!
Only common FACTORS can be eliminated from
the numerator and denominator.
Make sure
any expression you eliminate is a factor.
Simplifying Rational Expressions

Simplify the following expression.
x
x
x
5
35
7
2
)
5
(
)
5
(
7
x
x
x
x
7
Simplifying Rational Expressions
Example

Simplify the following expression.
20
4
3
2
2
x
x
x
x
)
4
)(
5
(
)
1
)(
4
(
x
x
x
x
5
1
x
x
Example

Simplify the following expression.
7
7
y
y
7
)
7
(
1
y
y
1
Example

Multiplying and
Dividing Rational
Expressions

Multiplying Rational
Expressions
Multiplying rational expressions
when P, Q, R, and S are
polynomials with Q
0 and S
0.
QS
PR
S
R
Q
P

Multiplying Rational
Expressions
Note that after multiplying such expressions, our result
may not be in simplified form, so we use the following
techniques.
Multiplying rational expressions
1)
Factor the numerators and denominators.
2)
Multiply the numerators and multiply the
denominators.

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- Spring '18
- Ma'am Arceo