Chapter 7 Rational Functions - College of the Redwoods

Section 7.2 Reducing Rational Functions 633
7.2 Exercises
In Exercises 1-12, reduce each rational
number to lowest terms by applying the
following steps:
i. Prime factor both numerator and denominator.
ii. Cancel common prime factors.
iii. Simplify the numerator and denominator
of the result.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
147
98
3087
245
1715
196
225
50
1715
441
56
24
108
189
75
500
100
28
98
147
1125
175
3087
8575
In Exercises 13-18, reduce the given expression
to lowest terms. State all restrictions.
13.
14.
15.
16.
17.
18.
x 2 − 10x + 9
5x − 5
x 2 − 9x + 20
x 2 − x − 20
x 2 − 2x − 35
x 2 − 7x
x 2 − 15x + 54
x 2 + 7x − 8
x 2 + 2x − 63
x 2 + 13x + 42
x 2 + 13x + 42
9x + 63
In Exercises 19-24, negate any two parts
of the fraction, then factor (if necessary)
and cancel common factors to reduce the
rational expression to lowest terms. State
all restrictions.
19.
20.
21.
22.
23.
x + 2
−x − 2
4 − x
x − 4
2x − 6
3 − x
3x + 12
−x − 4
3x 2 + 6x
−x − 2
8
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Version: Fall 2007