I'm attempting to find where the two peaks are given the following expression.

g(x,y):=(3 x^(2)*y^(2)+4 x^(2)*y+21 x^(2)-4 x*y^(2)-72 x*y-128 x+21 y^(2)+128 y+297)/((x^(2)+2 x+2) (y^(2)-2 y+2) (x^(2)-8 x+17) (y^(2)+8 y-17)):

There are two peaks found by viewing the graph of the expression above.  I've tried using the second derivative test, fsolve with no success. 

This is the command for fsolve i'm trying to use:

fsolve({(D[2](g))(x, y), (D[1](g))(x, y)},{x = -1.5 .. -.5, y = 1.7 .. 1.8})