1. Rational Expressions
Simplifying
Algebra B

2. Simplifying Rational Expressions
The objective is to be able to simplify a rational expression

3. Vocabulary Polynomial – The sum or difference of monomials.
Rational expression – A fraction whose numerator and denominator are polynomials.
Reduced form – a rational expression in which the numerator and denominator have no factors in common.

4. Simplifying Rational Expressions
Our aim is to cancel common factors
Factor the numerator and denominator and then cancel the common factors
We can cancel only factors NOT TERMS

5. Dividing Out Common Factors
Step 1 – Identify any factors which are common to both the numerator and the denominator.
The numerator and denominator have a common factor.
The common factor is the five.

6. Dividing Out Common Factors
Step 2 – Divide out the common factors.
The fives can be divided since 5/5 = 1
The x remains in the numerator.
The (x-7) remains in the denominator

7. Factoring the Numerator and Denominator
Factor the numerator.
Factor the denominator.
Divide out the common factors.
Write in simplified form.

8. Factoring
Step 1: Factor the numerator and denominator

9. Divide and Simplify x + 3 4 x 2
Step 2: Divide out the common factors. In this case, the common factors divide to become 1.
Step 5: Write in simplified form. x + 3 2 4 x

10. You Try It
Simplify the following rational expressions.

11. Problem 1 Factor the numerator and denominator
Divide out the common factors.
Write in simplified form.

12. Problem 2 Factor the numerator and denominator
You Try It
Problem 2
Factor the numerator and denominator
Divide out the common factors.
Write in simplified form.

13. Problem 3 Factor the numerator and denominator
You Try It
Problem 3
Factor the numerator and denominator
Divide out the common factors.
Write in simplified form.

14. Problem 4 Factor the numerator and denominator
You Try It
Problem 4
Factor the numerator and denominator
Divide out the common factors.
Write in simplified form.

15. Problem 5 Factor the numerator and denominator
You Try It
Problem 5
Factor the numerator and denominator
Divide out the common factors.
Write in simplified form.

16. Restrictions on Rational Expressions
For what value of x is undefined?
It is undefined for any value of “x” which makes the denominator zero.
The restriction is that x cannot equal 5.

17. YOU TRY IT
What are the excluded values of the variables for the following rational expressions?

18. Problem 1
Solution
y  0
z  0

19. Problem 2 Solution 2x - 12 = 0 ANSWER 2x - 12 + 12 = 0 + 12 x  6

20. Problem 3 Solution C2 + 2C - 8 = 0 Answer C  2 (C-2)(C+4) = 0 C  -4
C-2 = or C + 4 = 0
C-2+2 = C = 0 - 4
C = or C = -4
Answer
C  2
C  -4

21. HW
Pg. 463 #2 to 30 even