A higher number problem on the Equivalent Infinitesimal Substitution limx→0（sinx-tanx)/{[3√(1+X^2)-1][(1+sinx)-1]} Can the denominator be replaced by "x ^ 2 / 3" and "SiNx / 3" with the equivalent infinitesimal? Because the two equivalent infinitesimals are the same, the subtraction of the molecular part cannot be replaced, so the following steps are not very clear,

A higher number problem on the Equivalent Infinitesimal Substitution limx→0（sinx-tanx)/{[3√(1+X^2)-1][(1+sinx)-1]} Can the denominator be replaced by "x ^ 2 / 3" and "SiNx / 3" with the equivalent infinitesimal? Because the two equivalent infinitesimals are the same, the subtraction of the molecular part cannot be replaced, so the following steps are not very clear,

The denominator substitution is correct, SiNx / 3 can continue to be replaced by X / 3
sinx-tanx=tanx(cosx-1)~x*(-x^2/2)=-x^3/2(x->0)
So the final answer is Lim {X - > 0} (- x ^ 3 / 2) / (x ^ 3 / 9) = - 9 / 2