What is the limit as x approaches-3-of (x+1)/(x^2-9) ?

The limit as x approaches-3-of (x+1)/(x^2-9) is -infinity

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limit as x approaches-3-of (x+1)/(x^2-9)

x \to - 3 - lim (\frac{x + 1}{x ^{2} - 9})

- \infty

Solution steps

x \to - 3 - lim (\frac{x + 1}{x ^{2} - 9})

\frac{x + 1}{x ^{2} - 9} = (x + 1) \frac{1}{x ^{2} - 9}

= x \to - 3 - lim ((x + 1) \frac{1}{x ^{2} - 9})

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 - 3 - lim (x + 1) \cdot x \to - 3 - lim (\frac{1}{x ^{2} - 9})

x \to - 3 - lim (x + 1) = - 2

x \to - 3 - lim (\frac{1}{x ^{2} - 9}) = \infty

= (- 2) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

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What is the limit as x approaches-3-of (x+1)/(x^2-9) ?
The limit as x approaches-3-of (x+1)/(x^2-9) is -infinity