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

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

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

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

1

Solution steps

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

Simplify

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

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

Plug in the value

x = 1

= \frac{1}{1}

Simplify

= 1

x \to 0 lim (\frac{18}{x ^{2}})

\frac{d}{d x} (\frac{9}{( x - 8 ) ^{2}})

\frac{\partial}{\partial x} (3 x^{2} - 24 y)

\frac{d}{d x} (- 2 ln (x))

\frac{d}{d x} ((x - 2)^{3} (x - 6))

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