MTH 100
Rational Expressions & Functions;
Multiplying & Dividing
Key Ideas
1.
2.
3.
4.
What makes a rational function undefined?
Evaluating a rational function.
Reducing a rational function to lowest terms.
Multiplying and dividing rational functions.
Key Idea #1
1. You can’t divide by zero.
2. A rational function has a denominator; don’t
let the denominator be zero.
3. Find all the values that make the
denominator zero, and keep them out of the
domain.
Examples
2x  3
h( x ) 
4x  5
5x
g ( x)  2
x  5 x  66
Key Idea #2
Evaluating a rational function is no different that
evaluating any other function: plug the given
value in for the variable.
Key Idea #3
1. Factor the numerator and the denominator
completely.
2. Cancel common factors (one on the top, one
on the bottom).
3. You cannot cancel terms.
4. You cannot cancel parts of terms.
5. Important rule:
a b
ba
 1
Examples
3z  13z  30
2
3z  4 z  15
3
2
x  4 x  12 x
4
2
3x  12 x
3
x  125
20  4 x
2
Key Idea #4
• Very similar to Key Idea #3, don’t forget to flip
the second rational expression when you
divide.
Examples
x  8 2 x  12

x  6 3x  24
2
2
x  16 x  64 7 x  112

2
2
2 x  2 x  40 x  5 x  24
More Examples
2
2a
6

2
5a  5 a  1
2
2
2 x  8 x  24 15 x  47 x  14

2
2
2 x  17 x  30
5 x  x  42