Adding and Subtracting Rational Expressions Rational Functions In
Adding and Subtracting Rational Expressions
Rational Functions In mathematics, a rational function is any function which can be defined by a rational fraction, i. e. an algebraic fraction such that both the numerator and the denominator are polynomials. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective 1 Add rational expressions having the same denominator. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 3
Add rational expressions 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. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 4
EXAMPLE 1 Adding Rational Expressions with the Same Denominator Add. Write each answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 5
Objective 2 Add rational expressions having different denominators. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 6
Add rational expressions 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. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 7
EXAMPLE 2 Adding Rational Expressions with Different Denominators Add. Write each answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 8
EXAMPLE 3 Adding Rational Expressions Add. Write the answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 9
EXAMPLE 4 Adding Rational Expressions Add. Write the answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 10
EXAMPLE 5 Adding Rational Expressions with Denominators That Are Opposites Add. Write the answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 11
Objective 3 Subtract rational expressions. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 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 Slide 7. 4 - 13
EXAMPLE 6 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. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 14
EXAMPLE 7 Subtracting Rational Expressions with Different Denominators Subtract. Write the answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 15
EXAMPLE 8 Subtracting Rational Expressions with Denominators That Are Opposite Subtract. Write the answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 16
EXAMPLE 9 Subtracting Rational Expressions Subtract. Write the answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 17
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