How do you rationalize the denominator and simplify $\frac{6}{3 - \sqrt{11}}$ $6/(3-sqrt11)$ ?

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How do you rationalize the denominator and simplify $\frac{6}{3 - \sqrt{11}}$ $6/(3-sqrt11)$ ?

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Answer 1 · 2016-08-31T16:27:40

$\frac{6}{3 - \sqrt{11}} = - 9 - 3 \sqrt{11}$ $6/(3-sqrt(11)) =-9-3sqrt(11)$

Explanation:

Multiply both numerator and denominator by the radical conjugate $3 + \sqrt{11}$ $3+sqrt(11)$ of the denominator, then simplify...

$\frac{6}{3 - \sqrt{11}} = \frac{6 (3 + \sqrt{11})}{(3 - \sqrt{11}) (3 + \sqrt{11})}$ $6/(3-sqrt(11)) =(6(3+sqrt(11)))/((3-sqrt(11))(3+sqrt(11)))$

$\frac{6}{3 - \sqrt{11}} = \frac{6 (3 + \sqrt{11})}{3^{2} - {(\sqrt{11})}^{2}}$ $color(white)(6/(3-sqrt(11))) =(6(3+sqrt(11)))/(3^2-(sqrt(11))^2)$

$\frac{6}{3 - \sqrt{11}} = \frac{6 (3 + \sqrt{11})}{9 - 11}$ $color(white)(6/(3-sqrt(11))) =(6(3+sqrt(11)))/(9-11)$

$\frac{6}{3 - \sqrt{11}} = - 3 (3 + \sqrt{11})$ $color(white)(6/(3-sqrt(11))) =-3(3+sqrt(11))$

$\frac{6}{3 - \sqrt{11}} = - 9 - 3 \sqrt{11}$ $color(white)(6/(3-sqrt(11))) =-9-3sqrt(11)$

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How do you rationalize the denominator and simplify $\frac{6}{3 - \sqrt{11}}$ $6/(3-sqrt11)$ ?

1 Answer

Explanation:

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