1. Simplifying
Rational Expressions

2. Multiplying and Dividing Rational Expressions
Remember that a rational number can be expressed as a quotient of two integers. A rational expression can be expressed as a quotient of two polynomials.

3. Remember, denominators can not = 0.
Now,lets go through the steps to simplify a rational expression.

4. Step 1: Factor the numerator and the denominator completely looking for common factors.
Next

5. What is the common factor?
Step 2: Divide the numerator and denominator by the common factor.

6. Step 3: Multiply to get your answer.1
Step 3: Multiply to get your answer.

7. Looking at the answer from the previous example, what value of x would make the denominator 0?
The expression is undefined when the values make the denominator equal to 0

8. How do I find the values that make an expression undefined?
Completely factor the original denominator.

9. Factor the denominator
The expression is undefined when: a= 0, 2, and -2 and b= 0.

10. Lets go through another example.
Factor out the GCF
Next

11. 1 1

13. Now try to do some on your own.
Also find the values that make each expression undefined?

14. Remember how to multiply fractions:
First you multiply the numerators then multiply the denominators.

15. The same method can be used to multiply rational expressions.1

16. Step #1: Factor the numerator and the denominator.
Let’s do another one.
Step #1: Factor the numerator and the denominator.
Next

17. Step #2: Divide the numerator and denominator by the common factors.1

18. Step #3: Multiply the numerator and the denominator.
Remember how to divide fractions?

19. Multiply by the reciprocal of the divisor.1 5 4

20. Dividing rational expressions uses the same procedure.
Ex: Simplify

21. 1
Next

22. Now you try to simplify the expression:

23. Now try these on your own.

24. Here are the answers: