1. Adding and Subtracting Rational Expressions
Add rational expressions having the same denominator.
Add rational expressions having different denominators.
Subtract rational expressions. 1 2 3
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2. Add rational expressions having the same denominator.
Objective 1
Add rational expressions having
the same denominator.
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3. Add rational expressions having the same denominator.
We find the sum of two rational expressions with the same procedure that we used in Section 1.1 for adding two fractions having the same denominator.
If and (Q ≠ 0) are rational expressions, then
That is, to add rational expressions with the same denominator, add the numerators and keep the same denominator.
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4. EXAMPLE 1 Add. Write each answer in lowest terms. Solution:
Adding Rational Expressions with the Same Denominator
Add. Write each answer in lowest terms.
Solution:
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5. Add rational expressions having different denominators.
Objective 2
Add rational expressions having
different denominators.
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6. Add rational expressions having different denominators.
We use the following steps, which are the same as those used in Section 1.1 to add fractions having different denominators.
Step 1: Find the least common denominator (LCD).
Step 2: Rewrite each rational expression as an equivalent rational expression with the LCD as the denominator.
Step 3: Add the numerators to get the numerator of the sum The LCD is the denominator of the sum.
Step 4: Write in lowest terms using the fundamental property.
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7. EXAMPLE 2 Add. Write each answer in lowest terms. Solution:
Adding Rational Expressions with Different Denominators
Add. Write each answer in lowest terms.
Solution:
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8. EXAMPLE 3 Add. Write the answer in lowest terms. Solution:
Adding Rational Expressions
EXAMPLE 3
Add. Write the answer in lowest terms.
Solution:
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9. EXAMPLE 4 Add. Write the answer in lowest terms. Solution:
Adding Rational Expressions
EXAMPLE 4
Add. Write the answer in lowest terms.
Solution:
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10. EXAMPLE 5 Add. Write the answer in lowest terms. Solution:
Adding Rational Expressions with Denominators That Are Opposites
EXAMPLE 5
Add. Write the answer in lowest terms.
Solution:
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11. Subtract rational expressions.
Objective 3
Subtract rational expressions.
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12. Subtract rational expressions.
Use the following rule to subtract rational expressions having the same denominator.
If and (Q ≠ 0) are rational expressions, then
That is, to subtract rational expressions with the same denominator, subtract the numerators and keep the same denominator.
We subtract rational expressions having different denominators using a procedure similar to the one used to add rational expressions having different denominators.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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13. EXAMPLE 6 Subtract. Write the answer in lowest terms. Solution:
Subtracting Rational Expressions with the Same Denominator
Subtract. Write the answer in lowest terms.
Solution:
Sign errors often occur in subtraction problems. The numerator of the fraction being subtracted must be treated as a single quantity. Be sure to use parentheses after the subtraction sign.
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14. EXAMPLE 7 Subtract. Write the answer in lowest terms. Solution:
Subtracting Rational Expressions with Different Denominators
Subtract. Write the answer in lowest terms.
Solution:
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15. EXAMPLE 8 Subtract. Write the answer in lowest terms. Solution:
Subtracting Rational Expressions with Denominators That Are Opposite
Subtract. Write the answer in lowest terms.
Solution:
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16. EXAMPLE 9 Subtract. Write the answer in lowest terms. Solution:
Subtracting Rational Expressions
Subtract. Write the answer in lowest terms.
Solution:
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