Then use the equivalent expressions property to eliminate
factors common to both the numerator and the denominator.
A rational expression is
simplified
when 1 is the only common
factor of both the numerator and the denominator.
SIMPLIFYING RATIONAL EXPRESSIONS

Simplify:
Solution:
Factor.
Use (7
–
x
) =
–
(
x
–
7).
x
7.
SIMPLIFYING RATIONAL EXPRESSIONS
EXAMPLE

cont’d
SIMPLIFYING RATIONAL EXPRESSIONS

Simplify the following:

OPERATIONS ON RATIONAL EXPRESSIONS

Arithmetic operations are defined on rational expressions in the
same way as they are on rational numbers.
Definitions of Arithmetic Operations for Rational Expressions
For all rational expressions
and
where
Q
0 and
S
0,
Addition
Subtraction
OPERATIONS ON RATIONAL EXPRESSIONS

Multiplication
Division
Factoring and the equivalent expressions property of
rational expressions are used in the multiplication and
division of rational expressions.
OPERATIONS ON RATIONAL EXPRESSIONS

Multiply:
Solution:
Factor.
2
–
x
=
–
(
x
–
2).
EXAMPLE
OPERATIONS ON RATIONAL EXPRESSIONS

Simplify.
cont’d
OPERATIONS ON RATIONAL EXPRESSIONS

MATH10-3: Algebra
OPERATIONS ON RATIONAL EXPRESSIONS
Multiplication of Algebraic Expressions
Find the product:

MATH10-3: Algebra
OPERATIONS ON RATIONAL EXPRESSIONS
Division of Algebraic Expressions
Find the quotient:

Addition of rational expressions with a
common
denominator
is accomplished by writing the sum of the
numerators over the common denominator. For example,

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