What is the limit as x approaches 0 of (8/(1+x)-8)/x ?

The limit as x approaches 0 of (8/(1+x)-8)/x is -8

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limit as x approaches 0 of (8/(1+x)-8)/x

x \to 0 lim (\frac{\frac{8}{1 + x} - 8}{x})

- 8

Solution steps

x \to 0 lim (\frac{\frac{8}{1 + x} - 8}{x})

Simplify

\frac{\frac{8}{1 + x} - 8}{x} : - \frac{8}{1 + x}

= x \to 0 lim (- \frac{8}{1 + x})

Plug in the value

x = 0

= - \frac{8}{1 + 0}

Simplify

= - 8

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What is the limit as x approaches 0 of (8/(1+x)-8)/x ?
The limit as x approaches 0 of (8/(1+x)-8)/x is -8