copyright © 2010 pearson education, inc. all rights reserved sec 8.2 - 1 adding and subtracting...
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Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 8.2 - 1
Adding and Subtracting
Rational Expressions
Copyright © 2010 Pearson Education, Inc. All rights reserved.
Adding and Subtracting Rational Expressions
Rational Expressions
Adding or Subtracting Rational Expressions
Step 1 If the denominators are the same, add or subtract the numerators.
Place the result over the common denominator.
If the denominators are different, first find the least common
denominator. Write all rational expressions with this LCD, and then
add or subtract the numerators. Place the result over the common
denominator.
Step 2 Simplify. Write all answers in lowest terms.
Copyright © 2010 Pearson Education, Inc. All rights reserved.
Adding and Subtracting Rational Expressions
EXAMPLE 1 Adding and Subtracting Rational Expressions
with the Same Denominator
Add or subtract as indicated.
(a) 4m7
5n7
+
(b) 1
g3
5
g3–
Copyright © 2010 Pearson Education, Inc. All rights reserved.
Adding and Subtracting Rational Expressions
EXAMPLE 1 Adding and Subtracting Rational Expressions
with the Same Denominator
(c) a
a2 – b2
b
a2 – b2–
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Adding and Subtracting Rational Expressions
EXAMPLE 1 Adding and Subtracting Rational Expressions
with the Same Denominator
Add or subtract as indicated.
(d) 5
k2 + 2k – 15+ k
k2 + 2k – 15
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Adding and Subtracting Rational Expressions
The Least Common Denominator
Finding the Least Common Denominator
Step 1 Factor each denominator.
Step 2 Find the least common denominator. The LCD is the product of
all different factors from each denominator, with each factor raised
to the greatest power that occurs in the denominator.
Adding and Subtracting Rational Expressions
EXAMPLE 2 Finding Least Common Denominators
Assume that the given expressions are denominators of fractions. Find the
LCD for each group.
(a) 4m3n2, 6m2n5
Adding and Subtracting Rational Expressions
EXAMPLE 3 Adding and Subtracting Rational
Expressions with Different Denominators
Add or subtract as indicated.
(a)3z7
9z1+
The LCD of 3z and 9z is 9z.
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Adding and Subtracting Rational Expressions
EXAMPLE 3 Adding and Subtracting Rational
Expressions with Different Denominators
(b)y2
y – 43–
Adding and Subtracting Rational Expressions
Caution with Subtracting Rational Expressions
d + 5d – 6
d + 58d –
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Adding and Subtracting Rational ExpressionsEXAMPLE 4 Using the Distributive Property When
Subtracting Rational Expressions
e + 29
e – 22 –
Adding and Subtracting Rational ExpressionsEXAMPLE 6 Adding and Subtracting Three Rational
Expressions
Add.n2 + 3n
2n + 3
3 +n4+
Adding and Subtracting Rational Expressions
EXAMPLE 7 Subtracting Rational Expressions
Add.a2 + 2a – 3
a – 2 –a2 – 5a + 4
a + 2
Adding and Subtracting Rational Expressions
EXAMPLE 7Subtracting Rational Expressions
Add.a2 + 2a – 3
a – 2 –a2 – 5a + 4
a + 2