1. 5-3 Adding and subtracting rational functions
Chapter 5
5-3 Adding and subtracting rational functions

2. Objectives Add and subtract rational expressions.
Simplify complex fractions.

3. Adding and subtracting rational expressions
Adding and subtracting rational expressions is similar to adding and subtracting fractions. To add or subtract rational expressions with like denominators, add or subtract the numerators and use the same denominator.

4. Example #1
Add or subtract. Identify any x-values for which the expression is undefined.
x – 3
x + 4 +
x – 2

5. Example#2
Add or subtract. Identify any x-values for which the expression is undefined.
3x – 4
x2 + 1 –
6x + 1

6. Example#3
Add or subtract. Identify any x-values for which the expression is undefined.
3x2 – 5
3x – 1 –
2x2 – 3x – 2

7. Student guided practice
Do problems 2-4 in your book page 332

8. Adding and subtracting rational expressions
To add or subtract rational expressions with unlike denominators, first find the least common denominator (LCD). The LCD is the least common multiple of the polynomials in the denominators.

9. Finding LCM Find the least common multiple for each pair.
a. 4x3y7 and 3x5y4
b. x2 – 4 and x2 + 5x + 6

10. Adding and subtracting rational expressions
To add rational expressions with unlike denominators, rewrite both expressions with the LCD. This process is similar to adding fractions.

11. Example#4
Add. Identify any x-values for which the expression is undefined.
x – 3
x2 + 3x – 4 + 2x
x + 4

12. Example#5
Add. Identify any x-values for which the expression is undefined. x
x + 2 + –8
x2 – 4

13. Example#6
Add. Identify any x-values for which the expression is undefined. 3x
2x – 2 +
3x – 2
3x – 3

14. Example#7
Subtract Identify any x-values for which the expression is undefined.

15. Student guided practice
Do problems 7-10 in your book page 332

16. Complex fraction
Some rational expressions are complex fractions. A complex fraction contains one or more fractions in its numerator, its denominator, or both. Examples of complex fractions are shown below.
Recall that the bar in a fraction represents division. Therefore, you can rewrite a complex fraction as a division problem and then simplify. You can also simplify complex fractions by using the LCD of the fractions in the numerator and denominator.

17. Example Simplify. Assume that all expressions are defined. x + 2 x – 1

18. Example Simplify. Assume that all expressions are defined. 3 2 x – 1 x+

19. Example Simplify. Assume that all expressions are defined. 20 x – 1 6

20. Student guided practice
Do problems in your book page 332

21. Homework
Do problems even numbers from in your book page 332.

22. Closure Today we learned how to add and subtract rational expressions
Next class we are going to continue with rational functions.