CHAPTER 6
Rational Expressions
Source:
Elementary & Intermediate Algebra, Fourth Edition
Prepared and Edited by:
Dr. Mohamad Hammoudi

Topics of Chapter 6
6.1: Simplifying Rational Expressions.
6.2: Multiplication and Division of Rational
Expressions.
6.3: Addition and Subtraction of Rational
Expressions.
6.4: Complex Fractions.
6.5: Solving Rational Equations.
2

6.1: Simplifying Rational Expressions.
Objectives:
6.1.1: Evaluate rational expressions
6.1.2: Simplify rational expressions
3

6.1.1: Evaluate Rational Expressions
A rational number
is the ratio of two integers. Similarly, a
rational expression can be written as the ratio of two
polynomials, in which the denominator cannot have the value 0.
4

6.1.1: Evaluate Rational Expressions
Examples:
For what values of x is the following expression
undefined?
1.
2.
5

6.1.1: Evaluate Rational Expressions
Examples:
Using a calculator, evaluate the following
expressions for the given value of the variable.
1.
2.
6

6.1.2: Simplify Rational Expressions
We can always multiply or divide the numerator and
denominator of a fraction by the same nonzero number. The
same pattern is true in algebra.
The above two example are on equivalent fractions
7

6.1.2: Simplify Rational Expressions
Examples:
Simplify each rational expression. Assume the
denominators are not 0.
1.
2.
8

6.1.2: Simplify Rational Expressions
Examples:
Simplify each rational expression.
1.
2.
3.
9

6.1.2: Simplify Rational Expressions
Simplifying certain algebraic expressions involves recognizing a
particular pattern. Verify for yourself that
3
–
9 =
–
(9
–
3)
In general, it is true that a
–
b=
–
(
–
a + b)=
–
(b
–
a)=
–
1(b
–
a)
or, by dividing both sides of the equation by
b
–
a
,
10

6.1.2: Simplify Rational Expressions
Examples:
Simplify each rational expression.

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