Rewriting the equations:

(x+3)^2 - (x-2)(x+2)
Expand the terms:
= x^2 + 6x + 9 - (x^2 + 2x - 2x - 4)
= x^2 + 6x + 9 - x^2 - 4
= 6x + 5

a/(3a+3b) + a^2/(a^2-b^2)
Since a^2 - b^2 = (a+b)(a-b), the expression becomes:
= a/(3(a+b)) + a^2/[(a+b)(a-b)]
= a/(3(a+b)) + a/(a+b)
= (a + 3a)/(3(a+b))
= 4a/(3(a+b))

(5x-5y)/y / x^2-y^2 / y^2
Adjusting the division signs:
= (5x-5y)/y y^2 / (x^2-y^2)
= 5xy - 5y*y / x^2 - y^2
= 5xy - 5y^2 / (x+y)(x-y)