Diminishing MRTS Range, Follow Up Question

I have a directly related question to this thread (Diminishing MRTS range).

The production function in the example is defined as $f(K,L) = 600K^2l^2-K^3L^3$ and it is easy to show that MRTS = $-MPL over MPK $ = $ – 1200K^2L-3K^3L^2 over (1200KL^2-3K^2L^3)$= –$K over L$. Thus MTRS is diminishing (in absolute value) when K and L are positive.

A general formula for understanding whether MRTS is diminishing is as follows:

$frac{d frac{-f_L}{f_K}}{dL}$ = $frac{2f_{LK}f_{L}f_{K} – f_{LL}f_{K}^{2} -f_{KK}f_{L}^{2}}{f_{k}^{3}}$ > 0

Whether this is positive depends on the values of K and L. From this discussion, I think it should be positive for any K or L given that MRTS is diminishing for all L > 0. But when I plug in the appropriate values in the equation above for a given positive K and L (e.g. K = 10, L = 10) the equation is negative and therefore implies MRTS is not diminishing. I am certain I am just misunderstanding something. What am I doing wrong?