Let's break down the expression step by step:

First, we simplify the denominator:
√15 + √2 = √15 + √(4 * 1) = √15 + 2√1 = √15 + 2

Next, we simplify the numerator:
17 + 2(30)^1/2 = 17 + 2√30

Now we substitute both parts back into the original expression:
(17 + 2√30) / (√15 + 2)

Now we need to rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator:
[(17 + 2√30) / (√15 + 2)] * [(√15 - 2) / (√15 - 2)]

Expanding out the numerator and denominator gives us:
[(17√15 + 2√30 - 34) / (15 - 4)]

Simplifying further, we get:
(17√15 + 2√30 - 34) / 11

Therefore, the final simplified expression is:
(17√15 + 2√30 - 34) / 11