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

1 Answer
Jim H
Dec 4, 2015

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

Explanation:

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