# ap calculus

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Find the discontinuities of f(x)= ((x^2)+5x+6)/((x^2)-4)and categorize them as removable or non removable.

• ap calculus -

Start by finding the zeroes of the denominator.

• ap calculus -

since x^2+5x+6 = (x+2)(x+3)
and x^2-4 = (x+2)(x-2)

f(x) = (x+3)/(x-2) for x ≠ -2

so, x = -2 is a removable discontinuity,
x = 2 is a nonremovable discontinuity

extra credit: how do we remove the discontinuity at x = -2?

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