How do you rationalize the denominator and simplify $( 3sqrt6 + 5sqrt2)/(4sqrt6 - 3sqrt2)$ ?

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Answer 1 · 2018-03-23T12:45:04

$(102 + 29sqrt(12))/(78)$

$color(white)(xx)(3sqrt(6) + 5sqrt(2))/(4sqrt(6) - 3sqrt(2))$

$= ((3sqrt(6) + 5sqrt(2))(4sqrt(6) + 3sqrt(2)))/((4sqrt(6) - 3sqrt(2))(4sqrt(6) + 3sqrt(2)))$

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

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

$= (102 + 29sqrt(12))/(96 - 18)$

$= (102 + 29sqrt(12))/(78)$

Hence explained.

How do you rationalize the denominator and simplify ( 3sqrt6 + 5sqrt2)/(4sqrt6 - 3sqrt2)( 3sqrt6 + 5sqrt2)/(4sqrt6 - 3sqrt2)?