Simplify. Rationalize the denominator. 6/-4 + sqrt 3 ______

Find Conjugate: Select the conjugate of -4 + sqrt 3. Conjugate of a - sqrt(b): a + sqrt(b) Conjugate of -4 + sqrt 3: -4 - sqrt 3Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. To rationalize the denominator, we multiply both the numerator and the denominator by the conjugate of the denominator. 6/(-4 + sqrt 3) * (-4 - sqrt 3)/(-4 - sqrt 3)Simplify Numerator: Simplify the numerator by distributing the 6. 6 * (-4 - sqrt 3) = 6 * (-4) + 6 * (-sqrt 3) = -24 - 6sqrt(3)Simplify Denominator: Simplify the denominator using the difference of squares formula. (-4 + sqrt 3) * (-4 - sqrt 3) = (-4)^2 - (sqrt 3)^2 = 16 - 3 = 13Write Simplified Expression: Write the simplified expression. (-24 - 6sqrt(3)) / 13 This fraction is already in simplest form.

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Simplify. Rationalize the denominator. $\newline$ $\frac{6}{-4 + \sqrt{3}}$

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{6}{-4 + \sqrt{3}}

Find Conjugate: Select the conjugate of $-4 + \sqrt{3}$ . $\newline$ Conjugate of $a - \sqrt{b}$ : $a + \sqrt{b}$ $\newline$ Conjugate of $-4 + \sqrt{3}$ : $-4 - \sqrt{3}$
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. $\newline$ To rationalize the denominator, we multiply both the numerator and the denominator by the conjugate of the denominator. $\newline$ $\frac{6}{-4 + \sqrt{3}} \cdot \frac{-4 - \sqrt{3}}{-4 - \sqrt{3}}$
Simplify Numerator: Simplify the numerator by distributing the $6$ . $6 \times (-4 - \sqrt{3})$ $= 6 \times (-4) + 6 \times (-\sqrt{3})$ $= -24 - 6\sqrt{3}$
Simplify Denominator: Simplify the denominator using the difference of squares formula. $\newline$ $(-4 + \sqrt{3}) * (-4 - \sqrt{3})$ $\newline$ $= (-4)^2 - (\sqrt{3})^2$ $\newline$ $= 16 - 3$ $\newline$ $= 13$
Write Simplified Expression: Write the simplified expression. $\newline$ $(-24 - 6\sqrt{3}) / 13$ $\newline$ This fraction is already in simplest form.