What is the limit as x approaches-5-of (x+3)/(x+5) ?

The limit as x approaches-5-of (x+3)/(x+5) is infinity

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limit as x approaches-5-of (x+3)/(x+5)

x \to - 5 - lim (\frac{x + 3}{x + 5})

\infty

Solution steps

x \to - 5 - lim (\frac{x + 3}{x + 5})

\frac{x + 3}{x + 5} = (x + 3) \frac{1}{x + 5}

= x \to - 5 - lim ((x + 3) \frac{1}{x + 5})

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 - 5 - lim (x + 3) \cdot x \to - 5 - lim (\frac{1}{x + 5})

x \to - 5 - lim (x + 3) = - 2

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

= (- 2) (- \infty)

Apply Infinity Property:

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

= \infty

What is the limit as x approaches-5-of (x+3)/(x+5) ?
The limit as x approaches-5-of (x+3)/(x+5) is infinity