What are the removable and non-removable discontinuities, if any, of $f (x) = \frac{(x - 3) (x + 5)}{(x - 3) (x + 3)}$ $f(x)=((x-3)(x+5))/((x-3)(x+3))$ ?

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What are the removable and non-removable discontinuities, if any, of $f (x) = \frac{(x - 3) (x + 5)}{(x - 3) (x + 3)}$ $f(x)=((x-3)(x+5))/((x-3)(x+3))$ ?

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Answer 1 · 2015-12-04T18:44:57

There is a removable discontinuity at $x = 3$ $x=3$ and a non-removable discontinuity at $x = - 3$ $x=-3$ .

Explanation:

Any rational function is continuous on its domain.
Since the domain of this function is all reals except $3$ $3$ and $- 3$ $-3$ , $f$ $f$ has discontinuities at $3$ $3$ and $- 3$ $-3$ .

$lim_(xrarr3)f(x) = 8/6 = 4/3$ so the discontinuity at $3$ is removable.

$lim_(xrarr-3)f(x)$ does not exist, so the discontinuity at $-3$ is non-removable.

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What are the removable and non-removable discontinuities, if any, of $f (x) = \frac{(x - 3) (x + 5)}{(x - 3) (x + 3)}$ $f(x)=((x-3)(x+5))/((x-3)(x+3))$ ?

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Explanation:

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What are the removable and non-removable discontinuities, if any, of f(x)=((x-3)(x+5))/((x-3)(x+3))f(x)=(x−3)(x+5)(x−3)(x+3)f(x)=((x-3)(x+5))/((x-3)(x+3))?

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Explanation:

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What are the removable and non-removable discontinuities, if any, of $f (x) = \frac{(x - 3) (x + 5)}{(x - 3) (x + 3)}$ $f(x)=((x-3)(x+5))/((x-3)(x+3))$ ?