Simplify. Rationalize the denominator. 6/-9 - sqrt 5 ______

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Identify conjugate of denominator: Identify the conjugate of the denominator -9 - sqrt(5). The conjugate of a number of the form a - sqrt(b) is a + sqrt(b). Therefore, the conjugate of -9 - sqrt(5) is -9 + sqrt(5).Multiply by conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. To rationalize the denominator, we multiply the numerator and the denominator by the conjugate of the denominator. So, we have (6 * (-9 + sqrt(5)))/((-9 - sqrt(5)) * (-9 + sqrt(5))).Simplify numerator: Simplify the numerator. Now, we distribute the 6 across the conjugate in the numerator: 6 * (-9) + 6 * sqrt(5) = -54 + 6 * sqrt(5).Simplify denominator: Simplify the denominator using the difference of squares formula. The denominator simplifies as follows: (-9 - sqrt(5)) * (-9 + sqrt(5)) = (-9)^2 - (sqrt(5))^2 = 81 - 5 = 76.Write simplified expression: Write the simplified expression. Now we have the simplified expression: (-54 + 6 * sqrt(5))/76.Simplify fraction: Simplify the fraction by dividing each term in the numerator by the denominator. -54/76 + (6 * sqrt(5))/76 We can simplify -54/76 by dividing both numerator and denominator by 2: -27/38 + (6 * sqrt(5))/76.Check second term: Check if the second term can be simplified. The second term (6 * sqrt(5))/76 can be simplified by dividing both numerator and denominator by 2: 3 * sqrt(5)/38.Combine simplified terms: Combine the simplified terms. The final simplified expression is: -27/38 + 3 * sqrt(5)/38.

Simplify. Rationalize the denominator. $\newline$ $\frac{6}{-9 - \sqrt{5}}$

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Simplify. Rationalize the denominator. \newline6−9−5\frac{6}{-9 - \sqrt{5}}−9−5​6​

Simplify. Rationalize the denominator. $\newline$ $\frac{6}{-9 - \sqrt{5}}$