Simplify. Rationalize the denominator. 5/-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(5)Multiply 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)). 5/(-6 - sqrt(5)) * (-6 + sqrt(5))/(-6 + sqrt(5))Simplify Numerator: Simplify the numerator by distributing the multiplication. 5 * (-6 + sqrt(5)) = 5 * (-6) + 5 * (sqrt(5)) = -30 + 5sqrt(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 = 31Write Simplified Expression: Write the simplified expression. (-30 + 5sqrt(5))/31 This fraction is already in simplest form.

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

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{5}{-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})$\newline$. $\newline$ $\frac{5}{-6 - \sqrt{5}} \times \frac{-6 + \sqrt{5}}{-6 + \sqrt{5}}$
Simplify Numerator: Simplify the numerator by distributing the multiplication. $\newline$ $5 \times (-6 + \sqrt{5})$ $\newline$ = $5 \times (-6) + 5 \times (\sqrt{5})$ $\newline$ = $-30 + 5\sqrt{5}$
Simplify Denominator: Simplify the denominator using the difference of squares formula. $\newline$ $(-6 - \sqrt{5}) * (-6 + \sqrt{5})$ $\newline$ = $(-6)^2 - (\sqrt{5})^2$ $\newline$ = $36 - 5$ $\newline$ = $31$
Write Simplified Expression: Write the simplified expression. $\newline$ $(-30 + 5\sqrt{5})/31$ $\newline$ This fraction is already in simplest form.