Rational Expressions
Consider the following addition:
 The LCD is bd.
We can use this result as a rule for adding simple fractions in which the LCD is the
product of the denominators. A similar rule works for subtraction.
Adding or Subtracting Simple Fractions
If b ≠ 0 and d
≠ 0, then
Example 1
Adding and subtracting simple fractions
Use the rules for adding and subtracting simple fractions to find the sums and
differences.
Solution
a) For the numerator, compute ad + bc = 1 · 3 + 2 · 1 = 5. Use 2 3 or 6 for
the denominator:
Caution
The rules for adding or subtracting simple fractions can be applied
to any rational expressions, but they work best when the LCD is the product
of the two denominators. Always make sure that the answer is in its lowest terms. If
the product of the two denominators is too large, these rules are not helpful because
then reducing can be difficult.
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