(a²-9)/(a²+6a+9)+(a-3)/(a+3)-(a-a²)/(a²+2a-3)
=(a+3)(a-3)/(a+3)²+(a-3)/(a+3)-a(1-a)/(a-1)(a+3)
=(a-3)/(a+3)+(a-3)/(a+3)+a(a-1)/(a-1)(a+3)
=2(a-3)/(a+3)+a/(a+3)
=(2a-6+a)/(a+3)
=(3a-6)/(a+3)
(a²-9)/(a²+6a+9)+(a-3)/(a+3)-(a-a²)/(a²+2a-3)
=(a+3)(a-3)/(a+3)²+(a-3)/(a+3)-a(1-a)/(a-1)(a+3)
=(a-3)/(a+3)+(a-3)/(a+3)+a(a-1)/(a-1)(a+3)
=2(a-3)/(a+3)+a/(a+3)
=(2a-6+a)/(a+3)
=(3a-6)/(a+3)