1. Simplifying Rational Expressions
Objective: Identify values excluded from the domain of a rational expression. Simplify rational expressions.

2. Rational Expressions
The expression is an example of a rational expression.
A rational expression is an algebraic fraction whose numerator and denominator are polynomials.
Since division by zero is undefined, the polynomial in the denominator cannot be zero.

3. Example 1 State the excluded values for each rational expression.
b + 7  0
a2 – a – 12  0
2x + 1  0
2x  -1
b  -7
*Use your calculator
to find the zeros!
x  - ½
a  -3 or 4

4. Example 2
Suppose a cylinder has a volume of 770 cubic inches and a diameter of 12 inches. Find the height of the cylinder. Round to the nearest tenth.

5. Simplify Expressions
A rational expression is in simplest form when the numerator and denominator have no common factors except 1.
To simplify a rational expression, divide out any common factors of the numerator and denominator.

6. Example 3
Which expression is equivalent to .

7. Simplify Expressions
You can use the same procedure to simplify a rational expression in which the numerator and denominator are polynomials.

8. Example 4 Simplify . State the excluded values of x. x + 4 ≠ 0

9. Simplify Expressions
When simplifying rational expressions, look for binomials that are opposites.
For example 5 – x and x – 5 are opposites because 5 – x = -(x – 5).

10. Example 5
Simplify State the excluded values of x.
x – 5 ≠ 0
x ≠ 5

11. Simplify Expressions
Recall that to find the zeros of a quadratic function, you need to find the values of x when f(x) = 0.
The zeros of a rational function are found the same way.

12. Example 6
Find the zeros of f(x) =