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Simplify. Rationalize the denominator.
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Q. Simplify. Rationalize the denominator.
- Identify Conjugate: Identify the conjugate of the denominator .The conjugate of a number of the form is . Therefore, the conjugate of is .
- Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator.To rationalize the denominator, we multiply the fraction by a form of that consists of the conjugate of the denominator over itself. *
- Distribute Numerator: Distribute the numerator.Multiply by each term in the conjugate .
- Expand Denominator: Expand the denominator using the difference of squares formula.(-6 + \sqrt{5}) * (-6 - \sqrt{5}) = (-6)^2 - (\sqrt{5})^2\(\newline= 36 - 5= 31\)
- Write Simplified Expression: Write the simplified expression.The fraction with the rationalized denominator is .This fraction is already in its simplest form.
