To find the limit of LIM (x tends to 0) {(1 / x) - [1 / (e ^ x-1)]} by using the law of Robida,

To find the limit of LIM (x tends to 0) {(1 / x) - [1 / (e ^ x-1)]} by using the law of Robida,

1/x-1/(e^x-1)
=[e^x-1-x]/x(e^x-1)
Application of lobida's law
=(e^x-1)/[e^x-1+xe^x]
=e^x/(e^x+e^x+xe^x)
=1/2