Adding and Subtracting Rational Expressions
(Different Denominators)Add or subtract as indicated.
(a) The LCD for 2pand 8pis 8p.
Fundamental property(b) The LCD is
Fundamental propertyDistributive and commutative propertiesSubtract numerators.Combine like terms in the numerator.
NOW TRY=
r- 18
r 1 r- 32
=
6 r- 18 - 5 r
r 1 r - 32
=
6 r- 18
r 1 r- 32
-
5 r
r 1 r - 32
=
61 r- 32
r 1 r - 32
-
r# 5
r 1 r- 32
r 1 r- 32.6
r
-
5
r - 3
=
23
8 p
=
20 + 3
8 p
=
20
8 p
+
3
8 p
=
5 # 4
2 p# 4+
3
8 p
5
2 p
+
3
8 p
EXAMPLE 3
374 CHAPTER 7 Rational Expressions and Functions
Write the first fraction with
the common denominator.Add the numerators.
Keep the common denominator.CAUTION Sign errors occur easily when a rational expression with two or more
terms in the numerator is being subtracted. In this situation, the subtraction sign
must be distributed to every term in the numerator of the fraction that follows it.
Study Example 4carefully to see how this is done.
Subtracting Rational ExpressionsSubtract.
(a)
The denominators are the same. The subtraction sign must be applied to both
terms in the numerator of the second rational expression.
= Distributive property
7 x-x+ 2
3 x+ 1
=
7 x- 1 x- 22
3 x+ 1
7 x
3 x+ 1
-
x- 2
3 x+ 1
7 x
3 x+ 1
-
x- 2
3 x+ 1
EXAMPLE 4
Subtract the numerators.
Keep the common denominator.Use parentheses
to avoid errors.Be careful
with signs.NOW TRY
EXERCISE 3
Add or subtract as indicated.
(a)
(b)
3
z-
6
z- 52
3 x+
7
4 xNOW TRY ANSWERS
- (a) 1229 x (b) -z 13 zz-- 5152