Multiplying and Dividing Rational Expressions
Multiplying and dividing rational expressions follows the
same format as multiplying and
dividing fractions, the only difference is that you must factor the rational expressions
before simplifying the common factors.
You multiply fractions by multiplying across:
If possible, you can simplify
before multiplying – remember you must simplify in both the numerator and
denominator. For example:
Example 1: Multiply the rational expressions, be sure the answer is simplified:
Solution: The first step is to factor everything
completely, then get rid of the common
factors between the numerator and denominator.
Example 2: Multiply the rational expressions, be sure the answer is simplified:
Note: It is easiest (and best) to leave the answer in
factored form – it is not necessary to
multiply out the denominator.
Division of fractions is the same as multiplying the first fraction by the reciprocal of the
second fraction (always take the reciprocal of the fraction to the right of the division
Example 3: Divide – be sure the answer is simplified:
Solution: The first step is to change the division
problem to a multiplication problem.
The next step is to factor everything and multiply.
This section heavily depends on your factoring ability. Be
sure to review your factoring
worksheets, including how to factor the difference of squares and the sum/difference of
Multiply and divide the rational expressions – be sure all
answers are simplified
Remember order of operations for the last two problems: