5.4 multiply & divide rational expressions p.327 how do you simplify fractions made up of...
TRANSCRIPT
5.4 Multiply & Divide Rational Expressions
p.327
How do you simplify fractions made up of rational functions?
Simplified form of a rational expression -
• Means the numerator and denominator have NO common factors.
• If the numerator and/or denominator are polynomials, factor them ALL THE WAY, then “cancel” common factors. (x+?) or (x-?)
is a package deal—don’t break it up!
** Hint for simplifying:
FACTOR EVERYTHING FIRST!!
Factor Completely.Factor Completely.
1. 9x2 + 30x + 25
2. 4x2 -16x +16
3. 3x2 -17x +10
4. 3x3 - 4x2 -12x +16
5. 5x3 + 80
6. X3 + 3x2 - 9x - 27
(3x+5)2
4(x-2)2
(3x-2)(x-5)
(x+2)(x-2)(3x-4)
5(x3+16)
(x-3)(x+3)2
ExamplesExamples: Simplify.
2
2
x
5x a.
xxx
5)x(x
x
5x
1x
65x b.
2
2
x
1)-1)(xx(
1)6)(x-(x
1-x
6-x
2
43
22
32
18y
y10x
y2x
y6x c.
42
75
y36x
y60x
3
y5x 33
More Examples: Simplify.
3x
14x-3x
1-2x-3x
27x-3x d.
2
2
3 (Hint: Factor
everything first!!)
3x
1)-1)(x-(3x
1)1)(3x-(x
3x)-3x)(13x(1
1)1)(3x-3x(x
1)-1)(x3x)(3x-3x)(13x(1
21)-(3x-or 1)-3x)(3x-(1
Another example even yet: Simplify.
)46(9x827x
2x e. 2
3
x
4)6x-(9x4)6x-2)(9x(3x
2)(x 22
)469)(23(
)469)(2(2
2
xxx
xxx
23
2
x
x
Hey, how about ANOTHER Example!
x
xx
xx
xx
2
34
65
24 f.
2
2
2
x
xx
xx
xx
2
)1)(3(
)2)(3(
)2(2
)2)(3(2
)1)(3)(2(2
xxx
xxxx
)2(
)1)(2(
x
xx
)2(
)1)(2(
x
xx
1or )1( xx
You say you want MORE examples?
)4(4
3108 g. 2
2
2
xxx
xx
xxx
xx
22
2
4
1
4
3108
)14(4
)14)(32(3
xx
xx
34
32
x
x
THE LAST EXAMPLE!!!THE LAST EXAMPLE!!!
2
94)32(
2 h.
2
x
xx
x
x
)32)(32)(2(
)2)(32(
xxx
xxx
)32)(32(
)2(
1
)32(
)2(
xx
xx
x
x
32 x
x
• Find the surface area and volume of each tin.
• Calculate the ratio of surface area to volume for each tin.
• What do the ratios tell you about the efficiencies of the two tins?
A company makes a tin to hold flavored popcorn. The tin is a rectangular prism with a square base. The company is designing a new tin with the same base and twice the height of the old tin.
Packaging See page 328
• How do you simplify fractions made up of rational functions?
Factor and reduce
5.4 Assignment
p. 331
7-19 odd, 25-43 odd