I came across this very complex equation (calculating the Gaussian curvature of a surface): \begin{align*} 1 \not\equiv &-\frac{m}{2}\Bigl(\frac{3}{2}C+Su^{-1}-Tu^{-1}+2+Qu^{-1}\Bigr)\\ &\qquad\times(u^3C+Su^2-Tu^2)^{(-2u-2Q-5S+5T)/(6uC+4S-4T)} \\ &+\frac{m}{2}\Bigl[u^3(4C^2-3C)+u^2\Bigl(\frac{1}{3}TC-\frac{1}{3}SC-2S+2T-3QC\Bigr)\\ &\qquad\qquad+u(4TS-2S^2-2T^2-2QS+2QT)\Bigr]\\ &\qquad\times(u^3C+Su^2-Tu^2)^{(-2u-2Q-9S+9T-6uC)/(6uC+4S-4T)} \end{align*} I should somehow be able to prove that the right side of the equation is not identically equal to $1$. I would need some rule or something that "by eye" makes it obvious that it can not be $1$ (i.e. is not a constant function equal to $1$). $T$, $S$, $Q$, $C$ and $m$ are all constants (all the constants can not be zero, $m>2$ and must be integer, $T$ can not be equal to $S$ ); the only variable is $u$.

I thought that to be worth 1 certainly the functions that are "exponents" must vanish, so they should become zero, but the numerators of the two "exponents" being different, if one is zero (for some value of the constants) the other can not zero and therefore the formula will never be constant equal to 1.

Tips?