1. Chapter 7: Rational Expressions
Section 7.4: Adding and Subtracting Rational Expressions

2. Section 7.4: Adding and Subtracting Rational Expressions
Goal: To add and subtract rational expressions

3. Section 7.4: Adding and Subtracting Rational Expressions
To find 5/6 – 1/4, you must first find the least common denominator (LCD). The LCD is the least common multiple (LCM) of the denominators.
To find the LCM of two or more numbers or polynomials, factor each number or polynomial. The LCM contains each factor the greatest number of times it appears as a factor
LCM of 6 and 4 LCM of a2 – 6a + 9 and a2 + a – 12
6 = 2 · 3 a2 – 6a + 9 = (a – 3)2
4 = a2 + a – 12 = (a – 3)(a + 4)
LCM = 22 · 3 = LCM = (a – 3)2(a + 4)

4. Section 7.4: Adding and Subtracting Rational Expressions
Example 1
Find the LCM of 15a2bc3, 16b5c2, and 20a3c6

5. Section 7.4: Adding and Subtracting Rational Expressions
Add and Subtract Rational Expressions
As with fractions, to add or subtract rational expression, you must have common denominators
Specific Case
2/3 + 3/5
General case
a/c + b/d

6. Section 7.4: Adding and Subtracting Rational Expressions
Example 3
Simplify

7. Section 7.4: Adding and Subtracting Rational Expressions
Example 4
Simplify

8. Section 7.4: Adding and Subtracting Rational Expressions
Example 5
Simplify

9. Section 7.4: Adding and Subtracting Rational Expressions
Example 6
Simplify

10. Section 7.4: Adding and Subtracting Rational Expressions
Example 7
Simplify

11. Section 7.4: Adding and Subtracting Rational Expressions
Example 8
Simplify

12. Section 7.4: Adding and Subtracting Rational Expressions
Example 9
Find the slope of the line that passes through P(3/k, 1/3) and Q(1/2, 2/k)

13. Section 7.4: Adding and Subtracting Rational Expressions
Homework:
Practice Exercises: Pg. 325 #2 – 40 (even)