Algebra Rules Review Sheet Page 2
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REVIEW OF ALGEBRA
FRACTIONS
To add two fractions with the same denominator, we use the Distributive Law:
a
c
1
1
1
a
c
a
c
a
c
b
b
b
b
b
b
Thus, it is true that
a
c
a
c
b
b
b
But remember to avoid the following common error:
a
a
a
|
b
c
b
c
(For instance, take
a
b
c
1
to see the error.)
To add two fractions with different denominators, we use a common denominator:
a
c
ad
bc
b
d
bd
We multiply such fractions as follows:
a
c
ac
b
d
bd
In particular, it is true that
a
a
a
b
b
b
To divide two fractions, we invert and multiply:
a
b
a
d
ad
c
b
c
bc
d
EXAMPLE 3
x
3
x
3
3
(a)
1
x
x
x
x
2
2
3
x
3 x
2
x x
1
3x
6
x
x
x
2x
6
(b)
2
2
x
1
x
2
x
1 x
2
x
x
2
x
x
2
2
2
2
2
2
s
t
ut
s
t
u
s
t
(c)
u
2
2u
2
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