What is the limit as x approaches 0 of 5/(x^2+x)-5/x ?

The limit as x approaches 0 of 5/(x^2+x)-5/x is -5

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limit as x approaches 0 of 5/(x^2+x)-5/x

x \to 0 lim (\frac{5}{x ^{2} + x} - \frac{5}{x})

- 5

Solution steps

x \to 0 lim (\frac{5}{x ^{2} + x} - \frac{5}{x})

Simplify

\frac{5}{x ^{2} + x} - \frac{5}{x} : - \frac{5}{x + 1}

= x \to 0 lim (- \frac{5}{x + 1})

Plug in the value

x = 0

= - \frac{5}{0 + 1}

Simplify

= - 5

\frac{1}{2 - x}, 0

\frac{d}{d x} (\frac{4 x ^{2}}{x ^{2} - 1})

x^{3} + 7 x - 6

3 x

\int \frac{1}{z ^{2} - 1} d z

What is the limit as x approaches 0 of 5/(x^2+x)-5/x ?
The limit as x approaches 0 of 5/(x^2+x)-5/x is -5