Multiply and Divide Rational...
Transcript of Multiply and Divide Rational...
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Multiply and Divide
Rational ExpressionsLESSON 6.1
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Objective
Determine the domain of rational
expressions and functions
Simplify, multiply, and divide rational
expressions and functions
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Rational Expressions
A rational expression is the quotient (÷) of
two polynomials
EX: 𝑥−5
2𝑥+1
𝑥2−7𝑥−18
𝑥2−4
1
𝑥−3
2𝑎2+5𝑎𝑏+2𝑏2
𝑎2−6𝑎𝑏+8𝑏2
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Rational Expressions - Domain
REMEMBER: We cannot ÷0
Domain consists of all real numbers
except those for which the denominator
is zero.
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Rational Expressions - Domain
Determine the domain for each of the
following rational expressions
A. −3𝑧
𝑧+5B.
𝑛2−2𝑛−8
𝑛2−𝑛−12
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Rational Expressions - Domain
Determine the domain for each of the
following rational expressions
C. 𝑅 𝑥 =𝑥−3
𝑥2−2𝑥−8
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Rational Expressions - Simplify
Rational expressions can be simplified by
dividing out any common factors
EX: 10
10= 1
𝑥
𝑥= 1
𝑥−3
𝑥−3= 1
2 𝑥−3
3(𝑥−3)=
2
3
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Rational Expressions - Simplify
Simplify
D. 𝑥2+𝑥−6
2𝑥2−5𝑥+2E.
𝑦3+27
2𝑦2+6𝑦
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Rational Expressions - Multiply
MULTIPLYING RATIONAL EXPRESSIONS
1. Completely factor each polynomial
2. Divide out common factors
3. Multiply remaining terms (fractions)
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Rational Expressions - Multiply
F. 𝑛2−9
𝑛2+5𝑛+6×
𝑛+2
−2𝑛+6
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Rational Expressions - Multiply
G. 𝑎2−𝑏2
10𝑎2−10𝑎𝑏×
10𝑎+5𝑏
2𝑎2+3𝑎𝑏+𝑏2
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Rational Expressions - Divide
DIVIDING RATIONAL EXPRESSIONS𝑎𝑏𝑐𝑑
=𝑎
𝑏÷𝑐
𝑑=𝑎
𝑏×𝑑
𝑐
KFC→Keep the First, Flip the Second, Change the Sign
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Rational Expressions - Divide
H.
45𝑧4
7𝑦5𝑧
21𝑦2
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Rational Expressions - Divide
I.
𝑝3−8
5𝑝2+15𝑝
𝑝2−4
𝑝2+3𝑝
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Rational Expressions - Functions
Sometimes we are given two or more
functions and told to combine and
simplify them.
EX: 𝑓 𝑥
𝑔 𝑥𝑓 𝑥 ⋅ 𝑔(𝑥)
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Rational Expressions - Functions
J. 𝑓 𝑥 =𝑥2−9
2𝑥2−8𝑥𝑔 𝑥 =
𝑥−4
𝑥2+4𝑥+3ℎ 𝑥 =
𝑥2+6𝑥+9
𝑥2−5𝑥
1. Find 𝑓 𝑥 ⋅ 𝑔(𝑥)
2. Find 𝑓 𝑥
ℎ 𝑥