I have encountered a problem in Shafarevich's book and I have no clue:
Let $X$ be a hypersurface given by the equation $f_{m-1}(x_1,\cdots, x_n) + f_m(x_1,\cdots, x_n) = 0$ where $f_{m-1}$ and $f_m$ are non-zero homogeneous polynomials of degrees $m-1$ and $m$, respectively. Prove that if $X$ is irreducible, it is rational. (Shafarevich, Problem I.3.5.)