Simplify. Rationalize the denominator. 9/-5 + sqrt 5 ______

Find Conjugate: Select the conjugate of -5 + sqrt 5. Conjugate of a - sqrt(b): a + sqrt(b) Conjugate of -5 + sqrt 5: -5 - sqrt 5Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. To rationalize the denominator, we multiply the expression by (-5 - sqrt 5)/(-5 - sqrt 5). 9/(-5 + sqrt 5) * (-5 - sqrt 5)/(-5 - sqrt 5)Simplify Numerator: Simplify the numerator by distributing the multiplication. 9 * (-5 - sqrt 5) = 9 * (-5) + 9 * (-sqrt 5) = -45 - 9 sqrt 5Simplify Denominator: Simplify the denominator by using the difference of squares formula. (-5 + sqrt 5) * (-5 - sqrt 5) = (-5)^2 - (sqrt 5)^2 = 25 - 5 = 20Write Simplified Expression: Write the simplified expression. (-45 - 9 sqrt 5)/20 This fraction is already in simplest form.

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Simplify. Rationalize the denominator. $\newline$ $\frac{9}{-5 + \sqrt{5}}$

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{9}{-5 + \sqrt{5}}

Find Conjugate: Select the conjugate of $-5 + \sqrt{5}$ . $\newline$ Conjugate of $a - \sqrt{b}$ : $a + \sqrt{b}$ $\newline$ Conjugate of $-5 + \sqrt{5}$ : $-5 - \sqrt{5}$
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. $\newline$ To rationalize the denominator, we multiply the expression by $(-5 - \sqrt{5})/(-5 - \sqrt{5})$ . $\newline$ $\frac{9}{(-5 + \sqrt{5})} \times \frac{(-5 - \sqrt{5})}{(-5 - \sqrt{5})}$
Simplify Numerator: Simplify the numerator by distributing the multiplication. $\newline$ $9 \times (-5 - \sqrt{5})$ $\newline$ = $9 \times (-5) + 9 \times (-\sqrt{5})$ $\newline$ = $-45 - 9\sqrt{5}$
Simplify Denominator: Simplify the denominator by using the difference of squares formula. $\newline$ $(-5 + \sqrt{5}) * (-5 - \sqrt{5})$ $\newline$ $= (-5)^2 - (\sqrt{5})^2$ $\newline$ $= 25 - 5$ $\newline$ $= 20$
Write Simplified Expression: Write the simplified expression. $\newline$ $(-45 - 9 \sqrt{5})/20$ $\newline$ This fraction is already in simplest form.