I have three functions $f(y), g(y)$ and $h(x)$. I know that all three are positive valued and the first is increasing and the last two are decreasing. I also know that $$ g(y)=\frac{f(y)}{h(x)}.$$
The implicit funtion $y=F(x)$ is decreasing and I want to come up with an intuitive explanation of this fact. If we let $y$ increase, the $LHS$ decreases while the numerator in the $RHS$ increases. In order to maintain the equality, this calls for an increase in the denominator, which can only happen if $x$ is lower. Is this correct?
The way to solve this is to find the derivative with implicit differentiation. Then, use the properties defined above to show that the derivative has to be negative.