Download Because the denominator cannot equal 0, we must restrict values of

11 ACADEMIC
Lesson 3: Simplifying Rational Expressions
Date_______________
LEARNING GOAL: I will simplify rational expressions and determine any restrictions on the domain.
HW: p. 112 #1-3, 4bdf, 5, 6ce, 10, 13
If x and y are two integers, then the quotient
is a rational number with the restriction y ¹ 0
If P and Q are polynomials, then the quotient
is a rational expression with the restriction Q ¹ 0
Examples of rational numbers:
a)
b)
c)
Examples of rational expressions: a)
b)
c)
d)
e)
f)
RESTRICTIONS
Because the denominator cannot equal 0, we must restrict
values of x so that the denominator does not equal 0.
a)
5 - x  0, so x  5
d)
b)
0, so x  0
e)
c)
9 - x2  0, so x  3
f)
x  0, y  0
no
(x 0, so x1,-5
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11 ACADEMIC
Lesson 3: Simplifying Rational Expressions
Date_______________
SIMPLIFYING RATIONAL EXPRESSIONS
To simplify rational expressions we use the same techniques as with simplifying rational numbers:
Ex1.
Ex2.
Ex3.
Ex4.
30
42
(2)(3)(5)
=
(2)(3)(7)
(5)
= (1)(1)
(7)
5
=
7
Factor the numerator and the denominator into prime factors
Cancel factors common to both numerator and denominator
x2 - 2x
x2
x(x-2)
=
(x)(x)
x-2
=
x
Restriction: x  0
x2 - 9
x2 - 2x - 15
(x - 3)(x + 3)
=
(x - 5)(x + 3)
x-3
=
x-5
Restriction: x  -3 or 5
x2 + 7x - 8
2 - 2x
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