Variables $0\le x< 1$, $y,z\ge 0$. We have a constraint $$y=(z+c)\frac{x^2}{1-x},$$ where constant $c>0$.
We partitioned $x$ into $n$ intervals of equal length and defined a new variable $\phi_i=1$ for $i=1,\ldots,n$ iff $x\in(r_i-1,r_i]$ (we set $x=r_i$) and zero otherwise.
So we have this constraint $$y=\sum_{i=1}^n(z+c)\left(\frac{r_i^2}{1-r_i}\right)\phi_i$$
How can we linearize this new constraint?
If we define a new non-negative variable $\xi_i=z\phi_i$ and add the required 3 additional constraints with $M$, can we rewrite the second constraint above as $$y=\sum_{i=1}^n\left(\frac{r_i^2}{1-r_i}\right)(\xi_i+c\phi_i)$$