Did I perform this operation correctly?

Question

(a^2-b^2)/(a^2-2*a*b+b^2) /(2*a^2+5*a*b+3*b^2)/(2*a+3*b)
= 1/a-b

Answer 1

I get

[(a-b)(a+b) / (a+b)^2 ]
-----------------------
[(2a+3b)(a+b) / (2a+3b)]

[ (a-b) / (a+b) ]
= -------------------
[ (a+b) ]

= ( a-b) / (a+b)^2