How do you rationalize the denominator and simplify $\frac{3 \sqrt{6} + 5 \sqrt{2}}{4 \sqrt{6} - 3 \sqrt{2}}$ $( 3sqrt6 + 5sqrt2)/(4sqrt6 - 3sqrt2)$ ?

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How do you rationalize the denominator and simplify $\frac{3 \sqrt{6} + 5 \sqrt{2}}{4 \sqrt{6} - 3 \sqrt{2}}$ $( 3sqrt6 + 5sqrt2)/(4sqrt6 - 3sqrt2)$ ?

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Answer 1 · 2018-03-23T12:45:04

$\frac{102 + 29 \sqrt{12}}{78}$ $(102 + 29sqrt(12))/(78)$

Explanation:

$\times \frac{3 \sqrt{6} + 5 \sqrt{2}}{4 \sqrt{6} - 3 \sqrt{2}}$ $color(white)(xx)(3sqrt(6) + 5sqrt(2))/(4sqrt(6) - 3sqrt(2))$

$= \frac{(3 \sqrt{6} + 5 \sqrt{2}) (4 \sqrt{6} + 3 \sqrt{2})}{(4 \sqrt{6} - 3 \sqrt{2}) (4 \sqrt{6} + 3 \sqrt{2})}$ $= ((3sqrt(6) + 5sqrt(2))(4sqrt(6) + 3sqrt(2)))/((4sqrt(6) - 3sqrt(2))(4sqrt(6) + 3sqrt(2)))$

[Multiply Both Numerator and Denominator by $(4 \sqrt{6} + 3 \sqrt{2})$ $(4sqrt(6) + 3sqrt(2))$ ]

$= \frac{72 + 20 \sqrt{12} + 9 \sqrt{12} + 30}{{(4 \sqrt{6})}^{2} - {(3 \sqrt{2})}^{2}}$ $=(72 +20sqrt(12) + 9sqrt(12) + 30)/((4sqrt(6))^2 - (3sqrt(2))^2)$

$= \frac{102 + 29 \sqrt{12}}{96 - 18}$ $= (102 + 29sqrt(12))/(96 - 18)$

$= \frac{102 + 29 \sqrt{12}}{78}$ $= (102 + 29sqrt(12))/(78)$

Hence explained.

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How do you rationalize the denominator and simplify $\frac{3 \sqrt{6} + 5 \sqrt{2}}{4 \sqrt{6} - 3 \sqrt{2}}$ $( 3sqrt6 + 5sqrt2)/(4sqrt6 - 3sqrt2)$ ?

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Explanation:

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How do you rationalize the denominator and simplify $\frac{3 \sqrt{6} + 5 \sqrt{2}}{4 \sqrt{6} - 3 \sqrt{2}}$ $( 3sqrt6 + 5sqrt2)/(4sqrt6 - 3sqrt2)$ ?