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:

What should be multiplied times the denominator to eliminate the radical? The is still a radical in the result!

Try something a little different.

The radical has been eliminated!

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.

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

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

Example 2 Rationalize the denominator:

Numerators:

Denominators:

Putting it back together …