Suppose that we have the following equation:
$g = c\left( {\frac{{a + {\sigma ^2}}}{{b + {\sigma ^2}}}} \right)$
Is there anything that can be done to remove the $\sigma ^2$ term from the RHS of the equation so that the RHS $\rightarrow ca/b$, and the LHS of the equation has $\sigma ^2$ instead? Why or why not?
By dividing both sides by $\sigma ^2$, we get:
$\frac{g}{{{\sigma ^2}}} = c\left( {\frac{{\frac{a}{{{\sigma ^2}}} + 1}}{{b + {\sigma ^2}}}} \right)$
But this doesn't seem to get me any closer to my goal of removing the $\sigma ^2$ from the RHS. Maybe someone could point me in the right direction?