# Simplifying

Ultimately, reational expressions are nothing more than big fractions. Simplifying rational expressions works exactly the same way as aimplifying (or reducing) fractions. First you factor the numerator and denominator then you cancel any factors that they have in common. The examples show how it works.

## Example 1Simplify the expression .If we factor the numerator and denominator the expression becomes: Now we can cancel the two ## Example 3Simplify the expression .If we factor the numerator and denominator the expression becomes: Now we can cancel the two 2 We don't usually write out a 1 like that but, in this case, it helps to make it clearer why that's what's left. Now when we cancel the two 2 |
## Example 2Simplify the expression ?If we factor the numerator and denominator the expression becomes: If you're not sure how I factored the denominator the procedure is called factoring by grouping. You can find an explanation of the process in our polynomial short course. Now we can cancel the two Which of those versions, the factored or the multiplied out, is the simplified one is a matter of opinion. Some books and instructors prefer the first and others the second. ## Example 4Simplify the expression ?If we factor the numerator and denominator the expression becomes: If you're not sure how I factored the denominator the procedure is called factoring by grouping. You can find an explanation of the process in our polynomial short course. Now we can cancel the two Which of those versions, the factored or the multiplied out, is the simplified one is a matter of opinion. Some books and instructors prefer the first and others the second. |

## Dyanmic Tutorial - Simplifying Rational Expressions

**Directions:** This solution has ten steps. To see a description of each step click on the boxes on the left side below. To see the calculations, click on the corresponding box on the right side. Try working out the solution yourself and use the descriptions if you need a hint and the calculations to check your solution.