For the q-SDH problem, given the generator $g_1$ as a point on the elliptic curve, I can picture the $\beta g_1, \beta^2g_1, ..., \beta^qg_1$ since we can simply do the point adding $g_1$ multiple of $\beta$ times.
However, I cannot picture the point $\frac{1}{\beta+x}g_1$ (for some $x \in Z_p $). Is $\frac{1}{\beta+x}g_1$ a point on elliptic curve?
Moreover, in this q-SDH paper, there is a notation $g_1^{1/(x+c)}$. Is this $1/(x+c)$ equal a fraction $\frac{1}{x+c}$?
I cannot picture this $g_1^\frac{1}{x+c}$ either.