What is the limit as x approaches 0 of 1/(x-x^2)-1/x ?

The limit as x approaches 0 of 1/(x-x^2)-1/x is 1

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limit as x approaches 0 of 1/(x-x^2)-1/x

x \to 0 lim (\frac{1}{x - x ^{2}} - \frac{1}{x})

1

Solution steps

x \to 0 lim (\frac{1}{x - x ^{2}} - \frac{1}{x})

\frac{1}{x - x ^{2}} - \frac{1}{x} = \frac{1}{x - x ^{2}} (1 - \frac{\frac{1}{x}}{\frac{1}{x - x ^{2}}})

= x \to 0 lim (\frac{1}{x - x ^{2}} (1 - \frac{\frac{1}{x}}{\frac{1}{x - x ^{2}}}))

Simplify

\frac{1}{x - x ^{2}} (1 - \frac{\frac{1}{x}}{\frac{1}{x - x ^{2}}}) : \frac{1}{1 - x}

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

Plug in the value

x = 0

= \frac{1}{1 - 0}

Simplify

= 1

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What is the limit as x approaches 0 of 1/(x-x^2)-1/x ?
The limit as x approaches 0 of 1/(x-x^2)-1/x is 1