Arctan(2/(x^2y^2-1)) satisfies Laplace's equation?

[car202]

Homework Statement

Verify that $$\arctan(2/(x^2y^2-1))$$ satisfies Laplace's equation when $$x^2+y^2\ne 1$$.

You can also see at: (Problem 38)
http://books.google.ca/books?id=qh1...nepage&q=arctan(2/(x2y2-1)) laplacian&f=false

Homework Equations

The Attempt at a Solution

I really have no clue. I keep getting $$\frac{12x^4y^6-8x^2y^4-20y^2+12x^6y^4-8x^4y^2-20x^2}{(x^4y^4 - 2x^2y^2 + 5)^2}=\frac{4(x^2+y^2)(3x^2y^2-5)(x^2y^2+1)}{(x^4y^4 - 2x^2y^2 + 5)^2}$$, which is obviously not zero.

 

[Nino MMP]

I also tried \nabla^2f=\frac{\partial^2f}{\partial x^2} + \frac{\partial^2f}{\partial y^2} = 0, and I got something similar. I am really lost here. Any guidance would be appreciated.