1
Section 5.3  Addition and Subtraction of Rational Expressions
Addition
When we add or subtract rational expressions, we do it similarly to the way we do addition or
subtraction of fractions:
we have to have a common denominator.
If the denominators are the same, then you just add or subtract the numerators the way we add or
subtract polynomials.
The denominator stays the same.
After you finish adding or subtracting,
make sure to factor the numerator and denominator to see if anything cancels.
Examples:
Perform the given operations.
1.
8
5
8
3
+
1
8
8
8
5
3
=
=
+
=
2.
y
x
x
y
x
x
+
+
+
5
3
y
x
x
y
x
x
x
+
=
+
+
=
8
5
3
3.
1
4
4
3
1
4
3
11



x
x
x
x
2
1
4
)
1
4
(
2
1
4
2
8
1
4
5
3
3
11
1
4
)
5
3
(
3
11
=
=
+
=
+


=



=
x
x
x
x
x
x
x
x
x
x
The only complication happens when the denominators aren’t the same.
When that happens,
much like regular fractions, we need to get a common denominator.
Remember that when we
get a common denominator, we have to multiply both the numerator and the denominator by the
same amount so that we don’t unbalance our formula.
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 Spring '08
 Staff
 Rational Expressions, Addition, Fractions, Subtraction, Elementary arithmetic, common denominator

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