1. 7.4 Adding and Subtracting Rational Expressions

2. Adding and Subtracting Rational Expressions
To add or subtract rational expressions with like denominators, simply add or subtract their numerators and place the result over the common denominator.
Addition
Subtraction

3. Example 1
Example 2

4. Adding or Subtracting with Unlike Denominators
To add or subtract two rational expressions with unlike denominators:
Find the least common denominator, LCD.
Use the LCD to write additional factors.
Then, multiply each numerator by its additional factor and add or subtract
Addition
Subtraction is similar

5. Using Additional Factors
Example 3
1) Put 1 under anything which does not have a denominator. In this case, nothing needs to be done.
2) Factor the denominator.
3) Find LCD (least common denominator).
4) Write additional factors.
5) Multiply the numerator and additional factor and make the LCD the new denominator.

6. Example 4

7. Rewriting and Graphing Rational Functions
Rewrite the function:
Graph the function:

8. Simplifying Complex Fractions
A complex fraction is a fraction that contains a fraction in its numerator or denominator.
To simplify:
Method 1: Simplify the numerator and denominator by writing each as a single fraction. Then multiply the numerator by the reciprocal of the denominator.
Method 2: Multiply the numerator and the denominator by the LCD of every fraction in the numerator and denominator. Then simplify.

9. Example 5 Use method 1 Use method 2 3) Simplify.
3) Simplify.
1) Add fractions in the denominator.
2) Multiply the numerator by the reciprocal of denominator
Use method 2
1) Multiply numerator and denominator by LCD.
2) Simplify.

10. Example 6