Question

Find any points of discontinuity for each rational function. Sketch a graph. Describe any verticals or horizontal asympyoyes and any holes

(X^2-4)/(X+2)(X^2-49)

Answer 1

For
y = (x^2 -4)/((x +2)(x^2 -49))
the numerator factors to (x -2)(x +2), so the factor of (x +2) will cancel with that in the denominator, leaving
y = (x -2)/(x^2 -49)

There are points of discontinuity at the hole, x=-2, and at each of the vertical asymptotes, at x=-7, +7.
The horizontal asymptote is y=0.