Algebra 2 A
Section 8.1 Notes: Multiplying and Dividing Rational Expressions
A Rational Expression is a ratio of 2 polynomial expressions.
*Operations with rational numbers and rational expressions are similar.
*Just like reducing fractions, to simplify a rational expression, divide the numerator and denominator by a GCF.
*A rational expression is undefined when the denominator is equal to zero.
Example 1:
a) Simplify
3y  y  7
 y  7  y2  9
.
b) Under what conditions is the expression
Example 2:
a) Simplify
x  x  5
 x  5   x 2  16 
.
3y  y  7
 y  7  y2  9
undefined?
Under what conditions is the expression
Example 3: Simplify
x  x  5
 x  5   x 2  16 
undefined?
p2  2 p  3
.
p 2  2 p  15
For what value(s) of p is
p2  5 p  6
the expression undefined?
p 2  8 p  15
Example 4: Simplify
a 4b  2a 4
.
2a3  a3b
Example 5: Simplify
x 4 y  3x 4
.
2 x3  x3 y
Example 6: Simplify
8x
7 y2

.
21y 3 16 x3
Example 7: Simplify
10mk 2 5m5

.
3c 2 d 6c 2 d 2
*When given rational expressions to multiply or divide, if polynomials are present, factor them first!
*Once you are multiplying, cancel any factors that can be cancelled.
Example 8: Simplify
k 3
1 k 2
 2
.
k  1 k  4k  3
Example 9: Simplify
2d  6
d 3

.
d 2  d  2 d 2  3d  2
Example 10: Simplify
x  3 x 2  5x  6

.
x2
x2  9
Example 11: Simplify
3d  9
d 2

.
d 2  4 d  3 d 2  5d  4
*A complex fraction is a rational expression with a numerator and/or denominator that is also a rational expression.
*To simplify a complex fraction, first rewrite it as a division problem.
x2
9x2  4 y 2
.
Example 12: Simplify
x3
3x  2 y
a2
2
2
Example 13: Simplify a 49b .
a
a  3b