If we write sqrt(2) + sqrt(3) + 1/(2*sqrt(2) + 3*sqrt(3)) in the form (a*sqrt(2) + b*sqrt(3))/c such that a, b, and c are positive integers and c is as small as possible, then what is a + b + c?
Simplify: sqrt(2) + sqrt(3) + 1/(2*sqrt(2) + 3*sqrt(3))
Multiply both the numerator and the denominator by:
1/(2*sqrt(2) + 3*sqrt(3)) and factor
(17 sqrt(2) + 22 sqrt(3)) / 19
