Limx tends to 0 (1 / (ex power - 1) - 1 / x)

Limx tends to 0 (1 / (ex power - 1) - 1 / x)

lim {1/[e^(x^2)-1]-1/x}
=Lim [x + 1-e ^ (x ^ 2)] / {x [e ^ (x ^ 2) - 1)]} (denominator Equivalent Infinitesimal Substitution)
= lim [x+1-e^(x^2)]/x^3 (0/0)
= lim [1-2xe^(x^2)]/(3x^2) = ∞