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

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

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

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

1

Solution steps

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

Simplify

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

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

Plug in the value

x = 1

= \frac{1}{1}

Simplify

= 1

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