When constructing a sign table for a graph of function, if we have something like the following function or a derivative
$-\frac{3(6x^2+13x)}{(x-1)^2}$
Do we calculate the numerator and denominator expressions as negative, or just numerator
E. G. Table would table look like this
\begin{align} & -3(6x^2+13x)\\ &(x-1)^2\\ &f'(x)\\ \end{align}
In the expression $$-\frac{3(6x^2+13x)}{(x-1)^2}$$ the negative sign is NOT for both numerator and denominator, otherwise for the rule of the quotient of division the result would be positive.
Actually the previous expression must be intended as $$\frac{-3(6x^2+13x)}{(x-1)^2}$$ Thus if we have to solve $$\frac{-3(6x^2+13x)}{(x-1)^2}>0$$ we solve $-(6x^2+13x)>0\to 6x^2+13x<0\to -\frac{13}{6}<x<0$
as denominator is a square it is strictly positive for any $x$ so we can ignore it
Hope it is clear
