ap calculus
posted by Abby on .
Find the discontinuities of f(x)= ((x^2)+5x+6)/((x^2)4)and categorize them as removable or non removable.

Start by finding the zeroes of the denominator.

since x^2+5x+6 = (x+2)(x+3)
and x^24 = (x+2)(x2)
f(x) = (x+3)/(x2) 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?