2. Simplifying
Rational Expressions

3. Rational Expressions
a rational number can be expressed as a quotient of two integers. A rational expression can be expressed as a quotient of two polynomials.

4. Key concepts we need to know
Anything divided by itself is 1
Zero product property if (a)(b)=0 then a=0; b=0; or a and b=0
You can’t divide by 0!!!!

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

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

7. What value of x would make the denominator 0?
The expression is undefined when the values make the denominator equal to 0 so, we state restrictions to the domain.
x= -1,1

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

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

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

13. State Restrictions
What values of x will make the denominator =0?

14. 1 1

16. Now try to do some on your own.
Don’t forget to state the values that make each expression undefined?

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

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

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

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

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

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

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

24. 1
Next

25. Now you try to simplify the expression:

26. Now try these on your own.

27. Here are the answers: