1. 6-3: Complex Rational Expressions complex rational expression (fraction) – contains a fraction in its numerator, denominator, or both.

2. Method 1: Find LCD of all denominators, then multiply both the numerator and denominator by the LCD. LCD = y Distribute  Ex 1:  Multiply numerator and denominator by LCD

3. Ex 2: LCD = Distribute   or factor  Multiply numerator and denominator by LCD

4. Ex 3: LCD = Distribute   Factor  Multiply numerator and denominator by LCD

5. Ex 4: Rewrite with positive exponents Distribute    LCD = or factor  Multiply numerator and denominator by LCD

6. Ex 5: LCD = Distribute   Multiply numerator and denominator by LCD

7. Method 2: Simplify the numerator and denominator separately, then use division and multiply by reciprocal. LCD = Ex 6: Add fractions in numerator and denominator. Multiply by reciprocal  

8. Ex 7:  Factor   Multiply by reciprocal  Simplify the numerator and denominator

9. Ex 8:  Factor   Multiply by reciprocal  Simplify the numerator and denominator

10. Ex 9:  Factor   Multiply by reciprocal  Simplify the numerator and denominator

11. 6-3 Summary Method 1: Find LCD of all denominators, then multiply both the numerator and denominator by the LCD. Method 2: Simplify the numerator and denominator separately, then use division and multiply by reciprocal.     