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

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

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

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

\infty

Solution steps

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

\frac{x - 1}{x + 1} = (x - 1) \frac{1}{x + 1}

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

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

x \to - 1 - lim (x - 1) = - 2

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

= (- 2) (- \infty)

Apply Infinity Property:

- c \cdot (- \infty) = \infty

= \infty

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