Adding and Subtracting Rational Expressions with like Denominators

1. 1 2 12.6a Adding and Subtracting Rational Expressions with like Denominators Add rational expressions having the same denominator. Subtract rational expressions having the same denominator.

2. Objective 1 • Add rational expressions having • the same denominator.

3. 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. Add rational expressions having the same denominator.

4. EXAMPLE 1 Let’s start with basic fractions • Add. Write each answer in lowest terms. Solution:

5. EXAMPLE 2 If the expressions have the same (common) denominator, add or subtract the numerators, keep the same denominator, and simplify the result.

6. Objective 2 • Subtract rational expressions with like denominators.

7. 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. Subtract rational expressions. Use the following rule to subtract rational expressions having 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.

8. EXAMPLE 3 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.

9. Do the operations and simplify the result:

10. What’s Next Adding and Subtracting Rational Expressions with Different Denominators • Add. Write each answer in lowest terms. Solution:

11. Classwork/Homework