9­4 Day 1 Rational Expressions
May 05, 2009
9­4 Day 1 Rational Expressions
Objective:
Simplify rational expressions.
May 1­6:26 PM
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9­4 Day 1 Rational Expressions
May 05, 2009
Check Skills You'll Need
Factor.
1. 2x2 ­ 3x + 1
2. 4x2 ­ 9
3. 5x2 + 6x + 1
4. 10x2 ­ 10
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9­4 Day 1 Rational Expressions
May 05, 2009
Simplifying Rational Expressions
A rational expression is in simplest form when its numerator and denominator are polynomials that have no common divisors.
Examples (simplest form):
Examples (not simplest form):
1
x x 2(x ­ 3)
x2 x + 1 3(x ­ 3)
x 2
x ­ 1 x2 + 3
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9­4 Day 1 Rational Expressions
May 05, 2009
Example #1: Simplifying Rational Expressions
Simplify
x2 + 10x + 25
. State any restrictions on the variable.
2
x + 9x + 20
x2 + 10x + 25 (x + 5)(x + 5)
= (x + 4)(x + 5)
x2 + 9x + 20
(x + 5)(x + 5)
Step 2: Cancel common factors.
= (x + 4)(x + 5)
Step 1: Factor.
Step 3: Re­write the simplified expression.
(x + 5)
= (x + 4)
Step 4: Look at the original factored form to state the restrictions. The restrictions on x are needed to keep the denominator from becoming zero.
(x + 5)
(x + 4)
for x ≠ ­4 and x ≠ ­5
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9­4 Day 1 Rational Expressions
May 05, 2009
Example #2: Simplify each expression. State any restrictions on the variables.
a.
­27x3y
9x4y
b.
­6 ­ 3x
x2 ­ 6x + 8
c.
2x2 ­ 3x ­ 2
x2 ­ 5x + 6
May 1­6:30 PM
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9­4 Day 1 Rational Expressions
May 05, 2009
Example #3: One factor in designing a structure is the need to maximize the volume (space for working) for a given surface area (material needed for construction). Compare the ratio of the volume to surface area of a cylinder with radius r and height r to a cylinder with radius r and height 2r.
Use the formulas for volume and surface area of a cylinder.
Volume: V = πr2h
Surface Area: SA = 2πrh + 2πr2
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9­4 Day 1 Rational Expressions
May 05, 2009
May 1­6:31 PM
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9­4 Day 1 Rational Expressions
May 05, 2009
Homework: page 511 (1 ­ 6, 19 ­ 21, 42 ­ 43, 51 ­ 54)
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