(48x^6)/(48x^6/12x^2-12y^2)/(4x^5)/(3xy+3y^2)

You sure this is correct? It's very unusual to have

a/b/c/d

In addition,

(48x^6)/(48x^6/12x^2-12y^2) = 12(x^2-y^2)

. . .