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

Find Conjugate: Select the conjugate of -10 + sqrt 3. Conjugate of a - sqrt(b): a + sqrt(b) Conjugate of -10 + sqrt 3: -10 - sqrt 3Multiply 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 3)/(-10 - sqrt 3). 3/(-10 + sqrt 3) * (-10 - sqrt 3)/(-10 - sqrt 3)Simplify Numerator: Simplify the numerator by distributing the multiplication. 3 * (-10 - sqrt 3) = 3 * (-10) + 3 * (-sqrt 3) = -30 - 3sqrt(3)Simplify Denominator: Simplify the denominator using the difference of squares formula. (-10 + sqrt 3) * (-10 - sqrt 3) = (-10)^2 - (sqrt 3)^2 = 100 - 3 = 97Write Final Expression: Write the simplified expression with the rationalized denominator. (-30 - 3sqrt(3))/97 This fraction is already in simplest form.

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

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Algebra 2

Simplify radical expressions using conjugates

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Q. Simplify. Rationalize the denominator.

\newline

\frac{3}{-10 + \sqrt{3}}

Find Conjugate: Select the conjugate of $-10 + \sqrt{3}$ . $\newline$ Conjugate of $a - \sqrt{b}$ : $a + \sqrt{b}$ $\newline$ Conjugate of $-10 + \sqrt{3}$ : $-10 - \sqrt{3}$
Multiply by Conjugate: Multiply the numerator and the denominator by the conjugate of the denominator. $\newline$ To rationalize the denominator, we multiply the expression by $(-10 - \sqrt{3})/(-10 - \sqrt{3})$ . $\newline$ $\frac{3}{-10 + \sqrt{3}} \times \frac{-10 - \sqrt{3}}{-10 - \sqrt{3}}$
Simplify Numerator: Simplify the numerator by distributing the multiplication. $\newline$ $3 \times (-10 - \sqrt{3})$ $\newline$ = $3 \times (-10) + 3 \times (-\sqrt{3})$ $\newline$ = $-30 - 3\sqrt{3}$
Simplify Denominator: Simplify the denominator using the difference of squares formula. $\newline$ $(-10 + \sqrt{3}) * (-10 - \sqrt{3})$ $\newline$ $= (-10)^2 - (\sqrt{3})^2$ $\newline$ $= 100 - 3$ $\newline$ $= 97$
Write Final Expression: Write the simplified expression with the rationalized denominator. $\newline$ $(-30 - 3\sqrt{3})/97$ $\newline$ This fraction is already in simplest form.