I'm trying to fit a model with the written equation:

y = (a + bx + cx^2 + dx^3) / x

I'm aware to do a polynomial I'd do something like:

lm(y ~ poly(x, 4), dat)

But I'm drawing a blank on how to incorporate that divided term. Would I need to pre-calculate 1/x?

Feel free to demo on iris or mtcars or such like, or just write out the sort of "pseudo-code" without data as I have above!

If you are wondering, I am fitting that specific equation to replicate something that's done in my industry, but on my data, so that I can compare the two.