Simplify. Rationalize the denominator. 3/-10 - sqrt 5 ______

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Find Conjugate: Select the conjugate of -10 - sqrt(5). The conjugate of a - sqrt(b) is a + sqrt(b). So, the conjugate of -10 - sqrt(5) is -10 + sqrt(5).Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. To rationalize the denominator, we multiply the expression by (-10 + sqrt(5))/(-10 + sqrt(5)). This gives us (3 * (-10 + sqrt(5)))/((-10 - sqrt(5)) * (-10 + sqrt(5))).Simplify Numerator: Simplify the numerator. Multiplying 3 by each term in the conjugate -10 + sqrt(5) gives us: 3 * (-10) + 3 * sqrt(5) = -30 + 3sqrt(5).Simplify Denominator: Simplify the denominator using the difference of squares formula. The denominator is a difference of squares: (-10)^2 - (sqrt(5))^2. Calculating each term gives us: 100 - 5 = 95.Write Simplified Expression: Write the simplified expression. The simplified expression is (-30 + 3sqrt(5))/95. This fraction can be further simplified by dividing each term in the numerator by 5, the greatest common divisor of the numerator and the denominator.Divide by Common Divisor: Simplify the fraction by dividing by the greatest common divisor. Dividing each term in the numerator by 5 gives us: (-30/5) + (3/5)sqrt(5) = -6 + (3/5)sqrt(5). So the final simplified expression is (-6 + (3/5)sqrt(5))/95.Further Simplify Fraction: Simplify the fraction further by dividing the denominator. Since 95 is divisible by 5, we can simplify the fraction by dividing the denominator by 5: (-6 + (3/5)sqrt(5))/(95/5) = (-6 + (3/5)sqrt(5))/19.

Simplify. Rationalize the denominator. $\newline$ $\frac{3}{-10 - \sqrt{5}}$

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Simplify. Rationalize the denominator.\newline3−10−5\frac{3}{-10 - \sqrt{5}}−10−5​3​

Simplify. Rationalize the denominator. $\newline$ $\frac{3}{-10 - \sqrt{5}}$