1. Adding and Subtracting Rational Expressions

2. What is a Rational Expression?
a fraction in which the numerator and/or the denominator are polynomials.
We treat rational expressions just like we treat FRACTIONS!
Recall: How do we add/subtract fractions?

3. Adding/Subtracting Fractions Review
When fractions have a common denominator:
- add or subtract numerators
- keep denominator the same

4. You Try It!
Add or subtract the fractions:

5. When fractions have DIFFERENT denominators:
You must find a common denominator!
Easiest way to do this:
identify each denominator
Multiply each fraction (top AND bottom) by the OTHER denominator.
Then ADD or SUBTRACT numerators, keep denominator the same.

6. You Try It!
* To make a whole number into a fraction, simply make the denominator 1

7. Adding and Subtracting Rational Expressions:
What is a rational expression?
a fraction in which the numerator and/or the denominator are polynomials.
Examples:

8. Add/Subtract Rational Expressions
When fractions have a common denominator:
add or subtract numerators
keep denominator the same
When fractions have different denominators:
identify each denominator
Multiply each fraction (top AND bottom) by the OTHER denominator.

9. Example 1: Simplify

10. Example 2: Simplify

11. Example 3: Simplify

12. Your Turn! Simplify 

13. Example 4: Simplify

14. Example 5: Simplify

15. You Try It!

16. Real World Application: Work Problems
Taylor can paint a house by herself in 12 hours. Dan can paint a house by himself in 16 hours. How long would it take them to paint the house if they worked together?