Consider the following eq. Find value of x. Also, is this equation: Trancendental, Gauss Seidel, Newton-Raphson or Algebraic?

x=1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1.......infinity

here's a better look at what it looks like....

x=1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1/(x-1/(x+1 - Wolfram|Alpha

Any input would be really awesome.