What is the limit as x approaches 0 of 1/x-1/(x^3-x) ?

The limit as x approaches 0 of 1/x-1/(x^3-x) is diverges

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limit as x approaches 0 of 1/x-1/(x^3-x)

x \to 0 lim (\frac{1}{x} - \frac{1}{x ^{3} - x})

diverges

Solution steps

x \to 0 lim (\frac{1}{x} - \frac{1}{x ^{3} - 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}{x} - \frac{1}{x ^{3} - x}) = \infty

x \to 0 - lim (\frac{1}{x} - \frac{1}{x ^{3} - x}) = - \infty

= diverges

x \to 1 lim (\frac{1}{1 - x ^{3}})

x \to 4 lim (x^{2} + 3 x - 5)

x \to 2 lim ((x - 1)^{\frac{6}{( x - 2 )}})

y \to 0 lim (\frac{- 1}{∣ y ∣})

x \to \infty lim ((\frac{4 x ^{3} - 1}{3 x ^{2} + 2}) sin (\frac{1}{x}))

What is the limit as x approaches 0 of 1/x-1/(x^3-x) ?
The limit as x approaches 0 of 1/x-1/(x^3-x) is diverges