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6e reviewofalgebra.pdf


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2 ■ REVIEW OF ALGEBRA

FRACTIONS

To add two fractions with the same denominator, we use the Distributive Law:
a
c
1
1
1
a⫹c
⫹ 苷 ⫻ a ⫹ ⫻ c 苷 共a ⫹ c兲 苷
b
b
b
b
b
b
Thus, it is true that
a⫹c
a
c
苷 ⫹
b
b
b
But remember to avoid the following common error:
a
a
a
苷 ⫹
b⫹c
b
c

|

(For instance, take a 苷 b 苷 c 苷 1 to see the error.)
To add two fractions with different denominators, we use a common denominator:
a
c
ad ⫹ bc
⫹ 苷
b
d
bd
We multiply such fractions as follows:
a c
ac
ⴢ 苷
b d
bd
In particular, it is true that
⫺a
a
a
苷⫺ 苷
b
b
⫺b

a
b
a
d
ad
苷 ⫻ 苷
c
b
c
bc
d
EXAMPLE 3

(a)

x⫹3
x
3
3
苷 ⫹ 苷1⫹
x
x
x
x

(b)

3
x
3共x ⫹ 2兲 ⫹ x共x ⫺ 1兲
3x ⫹ 6 ⫹ x 2 ⫺ x
x 2 ⫹ 2x ⫹ 6



苷 2
2
x⫺1
x⫹2
共x ⫺ 1兲共x ⫹ 2兲
x ⫹x⫺2
x ⫹x⫺2

(c)

s2t
ut
s 2 t 2u
s2t 2


苷⫺
u
⫺2
⫺2u
2

Stewart: Calculus, Sixth Edition. ISBN: 0495011606. © 2008 Brooks/Cole. All rights reserved.

To divide two fractions, we invert and multiply: