Simplify. Rationalize the denominator. 9/-8 - sqrt 3 ______

Select Conjugate: Select the conjugate of -8 - sqrt(3). Conjugate of a - sqrt(b): a + sqrt(b) Conjugate of -8 - sqrt(3): -8 + sqrt(3)Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator to rationalize it. Expression to multiply: (-8 + sqrt(3)) Multiply (9) * (-8 + sqrt(3)) and (-8 - sqrt(3)) * (-8 + sqrt(3)) 9 * (-8 + sqrt(3)) / ((-8 - sqrt(3)) * (-8 + sqrt(3)))Simplify Numerator: Simplify the numerator by distributing the 9. 9 * (-8) + 9 * (sqrt(3)) = -72 + 9 * sqrt(3)Simplify Denominator: Simplify the denominator using the difference of squares formula. (-8)^2 - (sqrt(3))^2 = 64 - 3 = 61Write Simplified Expression: Write the simplified expression. (-72 + 9 * sqrt(3)) / 61 This fraction is already in simplest form.

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Simplify. Rationalize the denominator. $\newline$ $\frac{9}{-8 - \sqrt{3}}$

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{9}{-8 - \sqrt{3}}

Select Conjugate: Select the conjugate of $-8 - \sqrt{3}$ . $\newline$ Conjugate of $a - \sqrt{b}$ : $a + \sqrt{b}$ $\newline$ Conjugate of $-8 - \sqrt{3}$ : $-8 + \sqrt{3}$
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator to rationalize it. $\newline$ Expression to multiply: $(-8 + \sqrt{3})$ $\newline$ Multiply $(9) \times (-8 + \sqrt{3})$ and $(-8 - \sqrt{3}) \times (-8 + \sqrt{3})$ $\newline$ $9 \times (-8 + \sqrt{3}) / ((-8 - \sqrt{3}) \times (-8 + \sqrt{3}))$
Simplify Numerator: Simplify the numerator by distributing the $9$ . $9 \times (-8) + 9 \times (\sqrt{3}) = -72 + 9 \times \sqrt{3}$
Simplify Denominator: Simplify the denominator using the difference of squares formula. $\newline$ $(-8)^2 - (\sqrt{3})^2$ $\newline$ = $64$ - $3$ $\newline$ = $61$
Write Simplified Expression: Write the simplified expression. $\newline$ $(-72 + 9 \cdot \sqrt{3}) / 61$ $\newline$ This fraction is already in simplest form.