1. Rational Expressions Learning Targets: I can:
Simplify rational expressions.
Multiply, add, and subtract rational expressions.

2. Examples of Rational Expressions
A rational expression is nothing more than a fraction in which the numerator and/or denominator are polynomials. Here are some examples of rational expressions.
Examples of Rational Expressions

3. A rational expression has been reduced to lowest terms if all common factors from the numerator and denominator have been canceled. We already know how to do this with number fractions so let’s take a quick look at an example.

4. With rational expression it works exactly the same way.

5. In order to cancel a factor, it must be MULTIPLIED to the whole numerator and denominator.
So, the x + 3 above could cancel because it was multiplied to the whole numerator and denominator.
However, the x’s in the reduced form can’t be canceled since the x in the numerator is NOT MULTIPLIED to the -1.
Example: Plug in x = 4.

6. Example 1: Reduce the following rational expression to lowest terms.

7. Example 2: Reduce the following rational expression to lowest terms.

9. Example 1: Multiply each rational expression and reduce the answer to lowest terms.

10. Example 2: Multiply each rational expression and reduce the answer to lowest terms.

11. General Forms of Rational Expressions
Addition:
Subtraction:
As these have shown, we must remember that to ADD or SUBTRACT rational expressions, we must have COMMON DENOMINATORS.

12. Example 1: Simplify each expression.

13. Example 2: Simplify each expression.

14. Practice Problems
Rational Expressions Worksheet