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

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

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

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

1

Solution steps

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

Simplify

\frac{1}{x} - \frac{1}{x ^{2} + x} : \frac{1}{x + 1}

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

Plug in the value

x = 0

= \frac{1}{0 + 1}

Simplify

= 1

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