1. 8.3 Holes and Vertical Asymptotes

2. Points of Discontinuity (POD) : These are the values that make the factors in the denominator = 0. POD = Restricted Values = Excluded Values

3. Holes = Removable POD These are POD that have been removed from the denominator by cancelling away a factor. We write it with an “x = “, followed by the cancelled POD.

4. Vertical Asymptote = NON-Removable POD These are POD that have not been removed from the denominator by cancelling away a factor. We write it with an “x = “, followed by the NON-cancelled POD.

5. Ex) Find the POD, vertical asymptotes and holes of the graph of

8. Review: Finding POD, Excluded Values and Restricted Values These are values that make the factors in the denominator = 0 Factor denominator Set factors ≠0 REMEMBER TO SET EVERY FACTOR IN EVERY DENOMINATOR ≠ 0

9. Simplifying fraction. These are fractions that have no common factors in the numerator and denominator. Factor numerator AND denominator Cancel like factors REMEMBER YOU CAN ONLY CANCEL ONE IN THE NUMERATOR FOR ONE IN THE DENOMINATOR

10. Multiplying fraction. Factor numerators AND denominators Cancel like factors REMEMBER YOU CAN ONLY CANCEL ONE IN THE NUMERATOR FOR ONE IN THE DENOMINATOR.

11. Dividing fraction. Factor numerators AND denominators Change to MULTIPLY BY THE RECIPROCAL PROBLEM. Cancel like factors REMEMBER YOU CAN ONLY CANCEL ONE IN THE NUMERATOR FOR ONE IN THE DENOMINATOR.

12. Adding and Subtracting fractions Factor numerators AND denominators Get a common denominator by multiplying each fraction (TOP AND BOTTOM) by the missing factor of the other fraction. Write as a SINGLE FRACTION TOP: Add or Subtract Old Numerators BOTTOM: Common Denominator Multiply numerator out THEN simplify.

13. Complex Fractions Factor numerators AND denominators Multiply numerators by product of denominators Simplify new fraction

14. Solving EQUATION Factor denominators Multiply left and right side by product of denominators Solve for x