1. Simplify, Multiply and Divide Rational Expressions
12/5/2018 7:19 PM

2. Example 1
Simplify

3. Example 2 Simplify 2 1 2 1 Subtract exponents
variable stays where largest exponent is 1

4. Example 3
Simplify 8 5

5. Undefined Values
Any number substituted into a variable which makes the expression in the denominator equal to zero, it will cause the equation to be undefined.
Quick Steps:
FACTOR the expression
Solve the factors in the denominator for the variable
THESE are the restrictions
12/5/2018 7:19 PM

6. Example 4 (3x + 4) (3x + 4)(x – 1) Simplify
Identify any x-values for which the expression is undefined.
(3x + 4)
(3x + 4)(x – 1)
12/5/2018 7:19 PM

7. Example 6
Simplify Identify any x-values for which the expression is undefined.
If it is not in the order you usually see…switch it!!
–1(x2 – 4x)
x2 – 2x – 8
Factor out –1 in the numerator so that x2 is positive, and reorder the terms.
Factor the numerator and denominator. Divide out common factors.
Simplify.
12/5/2018 7:19 PM

8. Difference of two Squares!!!
Example 7
Simplify
Factor…Remember
Difference of two Squares!!!
Do NOT
Cancel the “x” or the “3”!!!!!
12/5/2018 7:19 PM

9. Rules of Multiplying Expressions
Factor numberator(s) and denominator(s)
Extend the fraction bar
Cancel [top/bottom] out the factors if needed and simplify.
12/5/2018 7:19 PM

10. Rules of Divide Expressions
KFC!!! Keep it (the first fraction), Flip it (the second fraction), Change it (the sign – division becomes multiplication)
Multiply and simplify!
12/5/2018 7:19 PM

11. Example 9
Simplify
12/5/2018 7:19 PM

12. Example 10 2 2
12/5/2018 7:19 PM

13. Example 11
Simplify
12/5/2018 7:19 PM

14. Example 12
Simplify
12/5/2018 7:19 PM