Simplify. Rationalize the denominator. 10/-9 - sqrt 3 ______

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Identify conjugate of denominator: Identify the conjugate of the denominator. The conjugate of a - sqrt(b) is a + sqrt(b). Therefore, the conjugate of -9 - sqrt(3) is -9 + sqrt(3).Multiply by conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. To rationalize the denominator, we multiply the fraction by a form of 1 that consists of the conjugate of the denominator over itself. (10/(-9 - sqrt(3))) * ((-9 + sqrt(3))/(-9 + sqrt(3)))Apply distributive property: Apply the distributive property (foil method) to the numerator. Multiply 10 by each term in the conjugate (-9 + sqrt(3)). 10 * (-9) + 10 * sqrt(3) = -90 + 10sqrt(3)Simplify numerator: Apply the distributive property (foil method) to the denominator. Multiply each term in (-9 - sqrt(3)) by each term in (-9 + sqrt(3)). (-9 * -9) + (-9 * sqrt(3)) - (sqrt(3) * -9) - (sqrt(3) * sqrt(3))Apply distributive property: Simplify the denominator. Calculate each multiplication in the denominator. 81 - 9sqrt(3) + 9sqrt(3) - 3 The middle terms cancel each other out, so we are left with: 81 - 3 = 78Simplify denominator: Write the simplified expression. The numerator is -90 + 10sqrt(3), and the denominator is 78. (-90 + 10sqrt(3)) / 78Write simplified expression: Simplify the fraction by dividing each term in the numerator by the denominator. Divide -90 by 78 and 10sqrt(3) by 78. -90/78 = -45/39 (simplifying by dividing both numerator and denominator by 2) 10sqrt(3)/78 = 5sqrt(3)/39 (simplifying by dividing both numerator and denominator by 2)Simplify fraction: Combine the simplified terms. The final simplified expression is: -45/39 + 5sqrt(3)/39

Simplify. Rationalize the denominator. $\newline$ $\frac{10}{-9 - \sqrt{3}}$

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Simplify. Rationalize the denominator. \newline10−9−3\frac{10}{-9 - \sqrt{3}}−9−3​10​

Simplify. Rationalize the denominator. $\newline$ $\frac{10}{-9 - \sqrt{3}}$