Simplify. Rationalize the denominator. 6/-6 + sqrt 5 ______

Find Conjugate: Select the conjugate of -6 + sqrt 5. Conjugate of a - sqrt(b): a + sqrt(b) Conjugate of -6 + sqrt 5: -6 - sqrt 5Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. To rationalize the denominator, we multiply the fraction by (-6 - sqrt 5)/(-6 - sqrt 5). 6/(-6 + sqrt 5) * (-6 - sqrt 5)/(-6 - sqrt 5)Simplify Numerator: Simplify the numerator by distributing the 6. 6 * (-6 - sqrt 5) = 6 * (-6) + 6 * (-sqrt 5) = -36 - 6sqrt(5)Simplify Denominator: Simplify the denominator using the difference of squares formula. (-6 + sqrt 5) * (-6 - sqrt 5) = (-6)^2 - (sqrt 5)^2 = 36 - 5 = 31Combine Numerator and Denominator: Combine the simplified numerator and denominator. (-36 - 6sqrt(5))/31 This fraction is already in simplest form.

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Simplify. Rationalize the denominator. $\newline$ $\frac{6}{-6 + \sqrt{5}}$

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{6}{-6 + \sqrt{5}}

Find Conjugate: Select the conjugate of $-6 + \sqrt{5}$ . $\newline$ Conjugate of $a - \sqrt{b}$ : $a + \sqrt{b}$ $\newline$ Conjugate of $-6 + \sqrt{5}$ : $-6 - \sqrt{5}$
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. $\newline$ To rationalize the denominator, we multiply the fraction by $(-6 - \sqrt{5})/(-6 - \sqrt{5})$ . $\newline$ $\frac{6}{-6 + \sqrt{5}} \times \frac{-6 - \sqrt{5}}{-6 - \sqrt{5}}$
Simplify Numerator: Simplify the numerator by distributing the $6$ . $6 \times (-6 - \sqrt{5}) = 6 \times (-6) + 6 \times (-\sqrt{5}) = -36 - 6\sqrt{5}$
Simplify Denominator: Simplify the denominator using the difference of squares formula. $\newline$ $(-6 + \sqrt{5}) * (-6 - \sqrt{5})$ $\newline$ $= (-6)^2 - (\sqrt{5})^2$ $\newline$ $= 36 - 5$ $\newline$ $= 31$
Combine Numerator and Denominator: Combine the simplified numerator and denominator. $\newline$ $(-36 - 6\sqrt{5})/31$ $\newline$ This fraction is already in simplest form.