1. Table of Contents Rationalizing Denominators With Two Terms In a previous modules we rationalized a single term denominator. We now turn our attention to rationalizing two term denominators. Example 1 Rationalize the denominator:

2. Table of Contents What should be multiplied times the denominator to eliminate the radical? The is still a radical in the result!

3. Table of Contents Try something a little different.

4. Table of Contents The radical has been eliminated!

5. Table of Contents The pattern we used was the original denominator … times the same two term expression, except for the opposite sign. These two expressions are called conjugates.

6. Table of Contents To rationalize a two term denominator multiply both numerator and denominator by the conjugate of the denominator. Back to our original problem - rationalize the denominator

7. Table of Contents Multiply both numerator and denominator by the conjugate of the denominator. Based on earlier work, we get … or

8. Table of Contents Example 2 Rationalize the denominator:

9. Table of Contents Numerators:

10. Table of Contents Denominators:

11. Table of Contents Putting it back together …

12. Table of Contents