Simplify. Rationalize the denominator. 3/-7 - sqrt 5 ______

Select Conjugate: Select the conjugate of -7 - sqrt 5. Conjugate of a - sqrt(b): a + sqrt(b) Conjugate of -7 - sqrt 5: -7 + sqrt 5Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator to rationalize it. (3) / (-7 - sqrt 5) * (-7 + sqrt 5) / (-7 + sqrt 5)Apply Distributive Property: Apply the distributive property to multiply the numerators and the denominators. Numerator: 3 * (-7 + sqrt 5) = -21 + 3*sqrt(5) Denominator: (-7 - sqrt 5) * (-7 + sqrt 5) = (-7)^2 - (sqrt(5))^2Simplify Denominator: Simplify the denominator. (-7)^2 - (sqrt(5))^2 = 49 - 5 = 44Write Simplified Expression: Write the simplified expression. (-21 + 3*sqrt(5)) / 44

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Simplify. Rationalize the denominator. $\newline$ $\frac{3}{-7 - \sqrt{5}}$

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Algebra 1

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{3}{-7 - \sqrt{5}}

Select Conjugate: Select the conjugate of $-7 - \sqrt{5}$ . $\newline$ Conjugate of $a - \sqrt{b}$ : $a + \sqrt{b}$ $\newline$ Conjugate of $-7 - \sqrt{5}$ : $-7 + \sqrt{5}$
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator to rationalize it. $\newline$ $(3) / (-7 - \sqrt{5}) * (-7 + \sqrt{5}) / (-7 + \sqrt{5})$
Apply Distributive Property: Apply the distributive property to multiply the numerators and the denominators. $\newline$ Numerator: $3 \times (-7 + \sqrt{5}) = -21 + 3\sqrt{5}$ $\newline$ Denominator: $(-7 - \sqrt{5}) \times (-7 + \sqrt{5}) = (-7)^2 - (\sqrt{5})^2$
Simplify Denominator: Simplify the denominator. $\newline$ $(-7)^2 - (\sqrt{5})^2 = 49 - 5 = 44$
Write Simplified Expression: Write the simplified expression. $\frac{-21 + 3\sqrt{5}}{44}$