Think this question is easy but I'm having much trouble to resolve it.
Let $\mathbb{R}(A/B)$ be the field of the racional funcions generated by $\frac{A}{B}$ over $\mathbb{R}$, where $A$ and $B$ are polynomials in $\mathbb{R}$. Then for all $\alpha,$ $\beta$, $\gamma$, $\delta$, satisfying $ \alpha \delta − \beta \gamma \neq 0$, we have $\mathbb{R}(A/B)$ $=$ $\mathbb{R}\left(\frac{\alpha A+\beta B}{\gamma A + \delta B}\right)$
Can someone help me or at least give a hint?
Hint: Write $A/B$ in the form \begin{bmatrix}A\\B\end{bmatrix} and now you have $$\begin{bmatrix}\alpha&\beta\\ \gamma&\delta\end{bmatrix}\begin{bmatrix}A\\B\end{bmatrix}=\begin{bmatrix}\alpha A+\beta B\\ \gamma A+\delta B\end{bmatrix}$$
If only the square matrix on the left were invertible, we could have so much fun..