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

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

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

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

5

Solution steps

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

Simplify

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

t \to 1 lim (t + 3)

f (x) = 2 x^{2} - 5 x + 3

x \to 0 + lim (ln (1 + x))

y = 5 tan (x), (\frac{π}{4}, 5)

f (x) = \frac{2}{x}, (- 4, - \frac{1}{2})

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