Multiplying Rational Expressions

Multiplying rational expressions is like doing so for number fractions, i.e. all the same rules apply. Basically you need to multiply all the numerators of all expressions in the multiplication, and then multiply all the denominators of all the involved expressions. Of course, you should simplify the final result when possible.




Example 1
Simplify the following expression.



Example 1 Solution
Multiplying all numerators together, then all denominators, followed by a simplification of the result, we get:



Don't forget to include values of x that the domain shouldn't take, as shown after the final result.

Example 2
Simplify the following expression.



Example 2 Solution
Following the prescribed methodology, we use the numerator and denominator from all three terms to get the following.






Dividing Rational Expressions


Division here is like doing so for number fractions, i.e. all the same rules apply. It's actually multiplication, except that you need to do two steps before you multiply. You need to look for terms that have '÷' or '/' just to the left of it. You need to invert these terms, i.e. the numerator and the denominator need to swap places. Then, change the operator from '÷' or '/' to '×', '*' or '.'. In short, change the division operator to the multiplication operator.

Example 1
Simplify the following expression.


Example 1 Solution
The term on the right has a division operator working on it, so once we invert it and change it to a multiplication operator, we get the following:



Example 2
Simplify the following expression.


Example 2 Solution
Remember, no matter how many terms there are in an expression that has the division operator on its left, you need to invert them and change the operator to a multiplication operator.



Example 3
Simplify the following expression.


Example 3 Solution
Given that there's only one term being divided, we invert that term and change its operator to a multiplication operator.





Return from Multiplying Rational Expressions to Advanced Algebra


Return Home to Algebra-by-Example.com



Unclear about a concept? Or see something missing?

Do you have questions about what you've read in this section? Is something missing? Post your question or contribution here and I'll get to it as soon as I can.

If you're sending in a problem you need help with, please also describe what you've tried to get a response.

Enter Your Title

Find a Local Algebra Tutor Today
Loading

Find a Local Algebra Tutor Today