Question

Determine whether the function has a vertical asymptote or a removable discontinuity. Classify the discontinuity. h(x)= (x^3+1)/(x+1)

Answer 1

in this case set the denominator to zero x+1=0, then solve for x.
X = -1
if you could factor the numerator and cancel something out you would find a hole or removable discontinuity. In this case, I don't see this as possible. Therefore, the vertical asymptote is x= -1

Hope this helps

Answer 2

The numerator can be factored since it's a convenient sum of cubes:
\[x^3+1^3=(x+1)(x^2-x+1)\]