Let $F$ be a field of characteristic zero. Assume that $a$ and $b$ are algebraic over $F$. The primitive element theorem says that there exists $w \in F(a,b)$ such that $F(a,b)=F(w)$; such $w$ is called a primitive element for the extension. A standard proof shows that $a+\lambda b$ is a primitive element for the extension for all but finitely many $F \ni \lambda$'s.
The exercise in this note says that $\lambda=1$ yields a primitive element, namely, $F(a,b)=F(a+b)$. I am not sure I know how to solve that exercise. Any hint will be appreciated.