To add these fractions together, we first need to find a common denominator. The common denominator for 2, 5, 6, and 10 is 10.

So we rewrite the fractions with a denominator of 10:

(3/2) (5/5) = 15/10
(6/5) (2/2) = 12/10
(5/6) (5/5) = 25/30
(3/10) (10/10) = 30/10
(42/25) * (2/2) = 84/50

Now we can add the fractions together:

15/10 + 12/10 - 25/30 + 30/10 + 84/50
= (15 + 12 - 25 + 30 + 84) / 10
= 116 / 10
= 11.6

Therefore, 3/2 * 6/5 + 5/6 - 3/10 + 42/25 equals 11.6.