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Published byLilian Lucas Modified over 6 years ago

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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:

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

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Try something a little different.

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The radical has been eliminated!

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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.

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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

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

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Example 2 Rationalize the denominator:

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Numerators:

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Denominators:

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Putting it back together …

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