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

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

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

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

- \frac{1}{8}

Decimal

- 0.125

Solution steps

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

Simplify

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

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

Plug in the value

x = 8

= - \frac{1}{8}

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