How do you rationalize the denominator and simplify $(sqrt5+2)/(3sqrt5-1)$ ?

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Answer 1 · 2016-04-18T17:18:53

$(13+5sqrt5)/44$

To rationalize, multiply with the conjugate of denominator, $3sqrt5 +1$ both in denominator and numerator. The result would be

$((sqrt5 +2) (3sqrt5 -1 ))/(45-1)$

= $(15 +5sqrt5 -2)/44$

= $(13+5sqrt5)/44$

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How do you rationalize the denominator and simplify (sqrt5+2)/(3sqrt5-1)(sqrt5+2)/(3sqrt5-1)?