If $w\in\mathbb{Q}(a,b)$, determine $w$ such that $\mathbb{Q}(w)=\mathbb{Q}(a,b)$ with $a,b\in\mathbb{R}$ and are algebraic over $\mathbb{Q}$

Question

I can see $\mathbb{Q}(w)=\mathbb{Q}(a,b)$ holds if $w$ is some rational linear combo of $a,b$ (like $w=a+b$) by using the fact that $\mathbb{Q}(w)(a)=\mathbb{Q}(a,b)=\mathbb{Q}(w)(b)$. But $w$ in general has form $q_1a^{n_1}b^{m_1}+q_2a^{n_2}b^{m_2}$ where $n_i, m_i\in\mathbb{Z}^+\bigcup\{0\}$ and $q_1, q_2\in\mathbb{Q}$. How can we discuss on the general case? Thanks in advance