WithTheFactorsOnBothSidesCancelled​(AngouriMath.​Entity,​AngouriMath.​Entity,​AngouriMath.​Entity.​Variable)

A polynomial that is not identically 0 has finitely many zeros, so it is not 0 anywhere
on a punctured neighbourhood of a point or of an infinity close enough in, and the two
quotients agree there. A factor analytic where it is defined and not identically 0 has
zeros that may gather at the destination but fill no interval, so the quotient with it
cancelled agrees with the other wherever the other is defined, and where it has a limit
the other has the same one. l'Hopital's rule turns ln(sinh(x)^3) into a quotient with
(e^x - e^(-x))^2 above and (e^x - e^(-x))^3 below, and (sinh(x)^3)^tan(x) at 0, which
is 1, was left unevaluated from each side for differentiating them. Differentiated instead, the factor is carried through the product
rule with everything beside it: (x - pi)^2 / ((x + tanh(x)) * (x - pi)) at +oo took
seven seconds, where x^2 / ((x + tanh(x)) * x), whose x the normalisation cancels, took
a fortieth of one; and ln(x + tanh(x)) / ln((x - pi)^2), which l'Hopital's rule turns
into the first, did not finish.