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^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?