I would like to take the result of a Reduce function call and eliminate any solutions that depend on the value of a particular variable (call it $y$). For instance, I am trying to get the parameters for a linear representation of the expression $\frac{y\beta}{\alpha+\beta}$ (linear in $y$), where $\alpha,\beta>0$. (Related: Force expression in certain form).
I do:
Reduce[y*β/(α + β) == a*y + b && α > 0 && β > 0, {y}, Reals] // FullSimplify
However, the command yields both the solution I'm looking for ($a=\frac{\beta}{\alpha+\beta},b=0$) and another, very specialized solution, where if $y$ happens to equal a specific combination of $a$ and $b$, then it does not matter what $a$ or $b$ are. While that is correct (and I applaud MMA for its completeness), I only want solutions that hold for any value of $y$. Also, the presence of that solution adds unwanted complexity to the Reduce output.
To reduce the cognitive load of determining exactly what to ignore in the output, I would like to get a further-reduced expression that eliminates any solution that depends on the value of $y$. Is there an easy way to do this?
