Precalculus Skill Builders Vol 1 Solutions

Example: Rationalize
45 .
Solution:
To rationalize the denominator you need to multiply both numerator and
denominator by the radical in the denominator. This is equivalent to
multiplying by 1 so it does not change the value of the expression.
4
5 = 4 5
5
= 4 5
5 5
Rationalize the following expressions.
12.
3
2
[ 3 2
2
] 13.
5
7
[ 5 7
7
] 14.
a 2 b 4
a 5 b 9
[ ab
ab ]
Example: Combine and simplify 2 3 + 1
2 3 .
Solution:
To combine rational expressions you first need to find a common denominator
and write the expression as one fraction. Then, you must rationalize the
denominator.
23 + 1 = 2!2 + 1 = 5 = 5 3
2 3 2 3 2 3 2 3 6
Rewrite the following as single, rationalized expression.
15.
3
2 + 6 2
[ 9 2
2
] 16.
6
8 + 3 8
[ 9 2
4
]
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