8.4
Multiply and Divide Rational Expressions
Simplified
form of a rational expression
A
rational expression in which its numerator and denominator have no common
factors (other than ±1)
SIMPLIFYING
RATIONAL EXPRESSIONS
Let a, b, and c be
nonzero real numbers or variable expressions. Then the following property applies.
Divide
out common factor c.
Example
1
Simplify
a rational expression
|
|
Factor numerator and
denominator. |
|
|
Divide out common factor. |
|
= _______ |
Simplified form. |
MULTIPLYING RATIONAL EXPRESSIONS
Let a, b, c, and d be nonzero real numbers or variable expressions. The rule
for multiplying rational expressions is the same as the rule for multiplying
numerical fractions: multiply _numerators_, multiply _denominators_,
and write the new fraction in simplified form.
Simplify,
if possible.
Example
2
|
|
Factor numerator and
denominator. |
|
|
Multiply numerator and
denominator. |
|
|
Divide out common
factors and write in simplified form. |
DIVIDING
RATIONAL EXPRESSIONS
To divide one rational
expression by another, multiply the first expression by the reciprocal of the
second expression.