What is the limit as x approaches 5 of (5/x-1)/(x-5) ?

The limit as x approaches 5 of (5/x-1)/(x-5) is -1/5

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limit as x approaches 5 of (5/x-1)/(x-5)

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

- \frac{1}{5}

Decimal Notation

- 0.2

Solution steps

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

Simplify

\frac{\frac{5}{x} - 1}{x - 5} : - \frac{1}{x}

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

Plug in the value

x = 5

= - \frac{1}{5}

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What is the limit as x approaches 5 of (5/x-1)/(x-5) ?
The limit as x approaches 5 of (5/x-1)/(x-5) is -1/5