Question

What are the removable and non-removable discontinuities, if any, of `f(x)=(2x^2+4x-6) / (x-1)`?

Answer 1

There is a removable discontinuity at `x=1`. That is the only discontinuity.

Explanation:

`f` is a rational function. Rational functions are continuous on their domains. The domain of `f` is `(-oo,1) uu (1,oo)`

So `f` is continuous except at `x=1`

`lim_(xrarr1) f(x) = lim_(xrarr1)((2x+6)(x-1))/(x-1)`

`=lim_(xrarr1)(2x+6)`

`= 2+6 = 8`

Because the limit exists, the discontinuity is removable.