Let $f,g\in\mathbb{C}[x_{1},...,x_{n}]$ be coprime homogeneous polynomials of degrees $d$ and $d-1$ over $\mathbb{C}$. Show that $V(f-x_{0}g)$ is a rational variety over $\mathbb{C}$, i.e. birationally equivalent to $\mathbb{P}^{n}_{\mathbb{C}}$.
I have no idea even where to start. Can somebody please give me a detailed explanation?