UNIT 11
Rational Expressions
9-4 Simplifying Rational Expressions
Simplest Form: means all terms are completely factored and any common terms
are reduced. (there should be no factorable polynomials remaining)
Examples:
1)
3x 2
3x 3  21x
2)
x2 4
x 2
3)
x 2  3x  2
x 2  x 6
4)
x 2 x 6
x 2 9
2)
4x 2  4x x 2  x  6

x 2  2x  3
4x
Multiply Rational Expressions:
Examples:
1)
5x 2 y 6x 3 y 2

2xy 3 10 y
x 2  x  2 3x  12
 2
3)
3x 2
x  6x  8
Divide Rational Expressions:
Examples:
1)
2x  2
x 2  2x
 2
3 x  12 x  6 x  8
3) 
3) (2 x 
2)
x 2  3x  2
( x 1)

4x 2
4x 2  9
x 5
9-5 Add & Subtract Rational Expressions
Examples:
1)
3)
7
5

6x 8x
4 3x 2  x  5

7x
14 x  21
2)
3
5

x 3 x 2
4)
2
x
5
 
x 2 3 x 2
5)
10 x
4
5


2
3x  3 x  1 6x
Complex Fractions:
EX 1:
1
3
x
5
4
y
2 3

x y
EX 3:
5 7

x y
EX 2:
3
5
y
x
UNIT 11
9-6
Rational Equations & Graphs
Part 2
Solve Rational Equations
Examples:
1)
7
x

x 3 4
2)
3)
5x
10
7
x 2
x 2
4)
5)
2
x

5 7

3 x
3x
12
 2
2
x 1 x 1
2
3
6

 2
x  10 x  2 x  12 x  20
Application:
1) If one student can complete the decorations for the prom in 5 days working
alone, another student could do it in 3 days, and a third could do it in 4 days,
how long would it take them working together?
2) A round trip flight took 3.9 h flying time. The plane traveled the 510 mi to
the city at 255 mi/h with no wind. How strong was the wind on the return
flight? Was the wind a head wind or a tail wind?
9-3
Graphs of Rational Functions
Examples: Determine any horizontal or vertical asymptotes
1)
1
x 5
2)
3 x 3  30
2x 3
3)
4x 2
x 3  x 2  2x