9.4 Multiplying and Dividing Rational Expressions
Factor the following perfect cube binomials:
1.) x 3 − 125
2.) 8 x 3 + 1
Which of the following can you simplify and why?
1.)
( x + 3)
3 x 2 ( x + 3)
2.)
x +1
x −1
3.)
x
x +1
Simplifying, Multiplying, and Dividing Polynomials
•
In order to fully simplify a polynomial you must factor every piece and
then see what you can cancel!
1.)
6 x 2 y 3 10 x 3 y 4
⋅
2 x 2 y 3 18 y 2
2.)
x 2 − 5x − 6
x2 −1
3.)
x 2 − 4 x − 12
x2 − 4
4.)
3 x − 27 x 3 3 x 2 − 4 x + 1
⋅
3x
3x 2 − 2 x − 1
5.)
x−3
⋅ (16 x 2 + 4 x + 1)
3
64 x − 1
9.4 Multiplying and Dividing Rational Expressions
Remember you NEVER DIVIDE fractions you always FLIP the fraction and
MULTIPLY!
1.)
3
x 2 + 3x
÷ 2
4x − 8 x + x − 6
2.)
6x 2 + 7 x − 3
÷ (2 x 2 + 3x)
2
6x
3.)
x
9 x 2 − 25
⋅ (3 x − 5) ÷
x+5
x+5
1
x2 − 9
x + 10
4.) 3
÷
⋅ 2
2
x + 3 x + 7 x + 12
x + 10 x
Homework: pg. 559 # 16-48 even
9.4 Multiplying and Dividing Rational Expressions
Skydiving
A falling skydiver accelerates until reaching a constant falling speed called
the terminal velocity. Because of air resistance, the ratio of the skydiver
volume to his or her cross-sectional surface area affects the terminal
velocity.
A.) The diagram shows a simplified geometric model of a skydiver with
maximum cross sectional surface area. Use the diagram to write a
model for the ratio of volume to cross sectional surface area for a
skydiver.
Body Part
Volume
Cross sectional
Surface Area
Arm or leg
Head
Trunk
Volume
=
SurfaceArea
B.) Use the result from part A to compare the terminal velocities of two
skydivers: One who is 60 inches tall and one who is 72 inches tall.
9.4 Multiplying and Dividing Rational Expressions