Calculus

Given
f(x) = (x^4 + 17) / (6x^2 + x - 1)
Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite (essential), or jump discontinuities.

From the work that I have done so far, I know that there are two discontinuiities, one at x = -1/2 and another at x = 1/3. On my graphing calculator, it appears that they form an infinite (or essential) discontinuity. Is this correct?

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  1. That is correct. In order to have a removable discontinuity, you need f(x) = 0/0 which is undefined, but may have a limit. In this case, the numerator is never zero.

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