What is the limit as x approaches-2-of (x-3)/(x^2-4) ?

The limit as x approaches-2-of (x-3)/(x^2-4) is -infinity

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limit as x approaches-2-of (x-3)/(x^2-4)

x \to - 2 - lim (\frac{x - 3}{x ^{2} - 4})

- \infty

Solution steps

x \to - 2 - lim (\frac{x - 3}{x ^{2} - 4})

\frac{x - 3}{x ^{2} - 4} = (x - 3) \frac{1}{x ^{2} - 4}

= x \to - 2 - lim ((x - 3) \frac{1}{x ^{2} - 4})

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 - 2 - lim (x - 3) \cdot x \to - 2 - lim (\frac{1}{x ^{2} - 4})

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

x \to - 2 - lim (\frac{1}{x ^{2} - 4}) = \infty

= (- 5) \cdot \infty

Apply Infinity Property:

- c \cdot \infty = - \infty

= - \infty

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What is the limit as x approaches-2-of (x-3)/(x^2-4) ?
The limit as x approaches-2-of (x-3)/(x^2-4) is -infinity