Question

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

Answer 1

`(13+5sqrt5)/44`

Explanation:

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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