Limit(7x+6x^2) / (7x^2+6x)

x->inf

divide top and bottom by x^2 to get

lim (7/x + 6)/(7 + 6/x)
as x ---> inf
both 7/x and 6/x ---> 0
so we are left with
(0 + 6)/(7 + 6) = 6/7