1. Simplify Rational Expressions
11.5
Simplify Rational Expressions

2. Rational Expression: a fraction whose numerators and denominators are polynomials.
Examples: , 2x , and x x2 – x2 + 1

3. Domain: the set of all real numbers except those for which the denominator is zero.
For example: The domain of is x all real numbers except -4.

4. Simplify Rational Expression the same way that you reduce a fraction.
Divide the numerator and denominator by “x”
2 5 =
Divide the numerator and denominator by “2”
2x + 4 =

5. Find the domain of each expression below.
Domain:x can be any real number except a number that would make the denominator 0!
Find the domain of each expression below.

6. How do you know when your rational expression is reduced?
Reduced Form: when the numerator and denominators have no common factors except for ±1.

7. The RULE: To simplify fractions, divide out common factors.
REMEMBER you can’t cancel out +(adding) and –(subtracting)

8. Remember you can only cancel out FACTORS!!!
For a,b,c any non-zero real numbers,
Remember you can only cancel out FACTORS!!!

9. Simplify the expression. Factor each polynomial.
x2 + 4x +4
Factor each polynomial.
x2 - 4
(x + 2)(x + 2) (x + 2)(x – 2)
What does the numerator and denominator have in common?
Factor out (x + 2)
The answer is: x x - 2

10. Simplify the expression.
Factor each polynomial.
x2 - 7x + 12 x2 +3x - 18
(x - 4)(x – 3) (x + 6)(x - 3)
What does the numerator and denominator have in common?
Factor out (x – 3)
The answer is: x x + 6