sqrt (2) + sqrt (3) + 1 / [ (2sqrt (2) + 3sqrt (3) ]
[(sqrt (2) + sqrt (3) ) ( 2sqrt ( 2) + 3 sqrt (3) ) + 1 ] / ( 2sqrt (2) + 3sqrt (3) )
[ 4 + 5sqrt (6) + 9 + 1 ] / ( sqrt (8) + sqrt (27))
[ 14 + 5sqrt (6) ] / ( sqrt 8 + sqrt (27) mult num/den by sqrt (8) - sqrt (27)
[14 + 5sqrt (6) [ sqrt (8) - sqrt (27)] / ( 8 - 27)
[14sqrt (8) + 5 sqrt (48) - 14sqrt(27) - 5sqrt (162) ] / (-19)
[ 14 * 2sqrt (2) + 5*4 sqrt (3) - 14*3 sqrt (3) - 5*9 sqrt ( 2) ] / (-19)
[ -17 sqrt 2 - 22 sqrt 3 ] / (-19)
[ 17 sqrt 2 + 22 sqrt (3) ] / 19
a = 17 b = 22 c =19
a + b + c = 58