What is the limit as x approaches 0 of 1/(1-e^x)-1/x ?

The limit as x approaches 0 of 1/(1-e^x)-1/x is diverges

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limit as x approaches 0 of 1/(1-e^x)-1/x

x \to 0 lim (\frac{1}{1 - e ^{x}} - \frac{1}{x})

diverges

Solution steps

x \to 0 lim (\frac{1}{1 - e ^{x}} - \frac{1}{x})

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

x \to 0 + lim (\frac{1}{1 - e ^{x}} - \frac{1}{x}) = - \infty

x \to 0 - lim (\frac{1}{1 - e ^{x}} - \frac{1}{x}) = \infty

= diverges

What is the limit as x approaches 0 of 1/(1-e^x)-1/x ?
The limit as x approaches 0 of 1/(1-e^x)-1/x is diverges