Calculate y = x / (1 + x ^ 2) on FPGA

I need to compute a function y=x/(1+x^2)

on a small FPGA at a fixed point, can you help me find the best algorithm?

I thought about these possibilities:

• since the FPGA is small i think i will use shift & add / subtract aa a multiplier and divider will use about the same number of cycles, right?
• This function is similar to digital filter, can I compute without separation using feedback?
• I don't think I will have a lot of memory, so I would rather not use LUT

Are there any other options? The timing requirement is not very strict, so I thought of a simple shift & subtraction, but if there is something simpler it might be better.