Section 11.4: Simplifying Rational Expressions
rational expression
a fraction whose numerator, denominator, or both are nonzero polynomials
example: 3x + 1
x2 + 1
simplifying a fraction
1. factor the numerator and denominator
2. then divide out any common factors
**A rational expression is undefined when the denominator is 0.
Examples:
1. 2x2 ­ 6x
6x2
2. 5(3 ­ x)
5x
3. 2x2
x(x + 5)
4. 4 ­ x2
x2 ­ x ­ 2
5. 12 ­ 5x
10x2 ­ 24x
6. x2 + x ­ 20
x2 + 2x ­ 15
7. x3 ­ x
x3 + 5x2 ­ 6x
For what values of the variable is the rational expression undefined?
8. 7
x ­ 3
9. 4
x2 ­ 1
10. x ­ 3
x2 + 5x ­ 6
Evaluate the expression.
11. 2x2 ­ 1 , when x = 1
x2 + 3
12. x2 + 4 , when x = 3
x ­ 2
A coin is tossed onto the large rectangular region shown. It is equally likely to land on any point in the region. Write a model that gives the probability that the coin will land in the shaded region. Then evaluate the model when x = 2.
13. 2x ­ 1
x ­ 1
x + 3
2x + 6