Find the maximum value of the function

f(x)=(x^2+9x-3) / x^2

I would simplify it first

f(x) = 1 + 9/x - 3/x^2
f ' (x) = -9/x^2 + 6/x^3
= 0 for a max/min

6/x^3 = 9/x^2
9x^3= 6x^2
9x^3 - 6x^2 = 0
3x^2(3x - 2) = 0
x = 0 , but that would make f(x) undefined, or
x = 3/2
f(3/2) = 1 + 9/(3/2) - 3/(9/4)
= 1 + 6 - 4/3 = 17/3