1. 6.4 Complex Fractions

2. Complex Fractions
A complex fraction is a fraction that has a fraction in its numerator or its denominator or both.
Examples:

3. Simplifying Complex Fractions
Method 1: Simplify the fraction by doing the operation indicated, then simplify.
Method 2: Eliminate the smaller fractions by multiplying both numerator and denominator by the LCD of the entire fraction.

4. Example 1 – Method 1
Division was the initial operation indicated. To perform this division, remember to multiply the numerator by the reciprocal of the denominator and then reduce.

5. Example 1 – Method 2
The LCD for the entire fraction is n3 because we are looking at n and n3. After you multiply both numerator and denominator by this LCD, just reduce.

6. Example 2 – Method 1
Do the operation indicated and subtract the two terms in the numerator. Then rewrite the division as a multiplication problem and simplify.

7. Example 2 – Method 2
Multiply both numerator and denominator by LCD of the entire fraction ( t ) and then simplify.

8. Example 3 – Method 1

9. Explanation of Example 3 – Method 1
Do the addition and subtraction indicated in the numerator and denominator.
Then rewrite the division in the form of multiplication.
Factor and reduce if possible.

10. Example 3 – Method 2

11. Explanation of Example 3 – Method 2
Multiply both numerator and denominator by LCD of entire fraction.
Then factor and simplify if possible.

12. Other instructions
Unless specified, you may use either Method 1 or 2, whichever one you prefer.
Please look at all of the examples in the book.
Please do assignment 6D for homework.