p.5 rational expressios
DESCRIPTION
P.5 RATIONAL EXPRESSIOS. ( التعبير الكسرية ). Objectives:. Simplify Rational Expression Operations on Rational Expressions Determining the LCD of Rational Expressions Complex Fractions. Polynomial – The sum or difference of monomials. - PowerPoint PPT PresentationTRANSCRIPT
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P.5 RATIONAL EXPRESSIOS
Objectives:
Simplify Rational Expression
Operations on Rational Expressions
Determining the LCD of Rational Expressions
Complex Fractions
التعبير )(الكسرية
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Polynomial – The sum or difference of monomials. Rational expression – A fraction whose numerator
and denominator are polynomials. Domain of a rational expression – the set of all real
numbers except those for which the denominator is zero.
Reduced form – a rational expression in which the numerator and denominator have no factors in common.
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Rational Function:
Let p(x) and q(x) be polynomials. Then a rational function is given by:
p xf x
q x
The domain (values x can take) of the fcn includes all x-values such that q(x) 0.
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Ex: Find the domain:
The domain of f is all values of x, … but x2 - 4 0; solve by factoring … (x - 2)(x + 2) 0; By ZPP, x-2 0; x+2 0 x 2
2
2
5. ( )
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xa f x
x
, 2 2,2 2, Domain=
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solve: x2 + 1 0
x2 -1
No real solutions …. There are no restrictions on the values x can take.
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4. ( )
1b f x
x
1x
Domain = ,
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Rational Expressions
P, Q, R, and S are polynomials
Addition
Operation
Multiplication
Subtraction
Division
P Q P Q
R R R
P Q P Q
R R R
P Q PQ
R S RS
P Q P S PS
R S R Q RQ
Notice the common denominator
Find the reciprocal and multiply
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Cancellation Properties
ac bc a b c implies if 0
acbc
ab
b c if 0 0,
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Rational Expressions
Ex: Simplify
2
2
25
7 10
x
x x
5 5
2 5
x x
x x
Cancel common factorsFactor
Ex: Simplify
2 2
3 2
2 1 6 6
1
x x x x
x x
3
1 1 6 1
1 1
x x x x
x xx
FactorCancel common factors
Multiply Across
5
2
x
x
2
6 1x
x
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Least Common Denominator( LCD)
LCD P LCD RP R Q SQ S LCD
product of all prime factors in and
raised to the highest power.
LCD P Q
المشترك ) المقام(االصغر
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Adding/Subtracting
Ex: Simplif4
3 2
yx x
Combine like terms
3 4 2
( 4) 4
x x
x x x x
Must have LCD: x(x + 4)
3 12 2 5 12
( 4) 4
x x x
x x x x
Distribute and combine fractions
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Complex Fractions
Ex: Simplify
32
9
4 x
xx
Factor to get hereDistribute and reduce to get here
32
94
xx
x xx
2
3 2
9 4
x
x
Multiply by the LCD: x
3 2 1
3 2 3 2 3 2
x
x x x
المركبة ) (الكسور
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Ex: Simplify
12 12 3
2 3 2
2 2
9 3 9 27
64 5 24
a a a a
a a a
21 2 3 11 4
3 1 5
x x
x x x
1 1
2 2
xy yx
x y