6.3 Adding and Subtracting Rational Expressions
Objective 1: Add and Subtract Rational Expressions with Common Denominators
When adding or subtracting fractions, we need a common denominator.
Adding and Subtracting Rational Expressions with Common Denominators
P
R
If
and
are rational expressions, then
Q
Q
P R PR
P R PR
and
.
 
 
Q Q
Q
Q Q
Q
6.3.5 Perform the indicated operation and simplify the result. Leave your answer in factored
form.
Objective 2: Find the Least common Denominator of Rational Expressions
Finding the Least Common Denominator (LCD) of Rational Expressions
Step 1.
Step 2.
Step 3.
Factor each denominator completely.
List each unique factor from any denominator.
The least common denominator is the product of the unique factors, each raised to a
power equivalent to the largest number of times that the factor occurs in any one denominator.
6.3.12 Find the least common denominator (LCD) for the rational expressions.
Objective 3: Add and Subtract Rational Expressions with Unlike Denominators.
To add numeric fractions with unlike denominators, start with finding the LCD.
Then multiply terms by a form of one (p/p) to get the LCD in the denominator of each term.
5 1  5   3   1   4  15 4 15  4 9 3
         




8 6  8   3   6   4  24 24
24
24 8
We add and subtract rational expressions in much the same way. We start by determining the least
common denominator (LCD).
Adding and Subtracting Rational Expressions with Unlike Denominators
Step 1.
Step 2.
Step 3.
Step 4.
Find the LCD for all expressions being added or subtracted.
Write equivalent expressions for each term using the LCD as the denominator.
Add/subtract the numerators, but keep the denominator the same (the LCD).
Simplify if possible.
6.3.16 Add or subtract as indicated and simplify the result.
6.3.28 Add or subtract as indicated and simplify the result.
6.3.33 Add or subtract as indicated and simplify the result.