Setting the denominator to zero can help find the points of discontinuity for the rational function.
The denominator is (x+9)(x+7). Equating each factor to zero, the results are:
x+9 = 0; x=-9
x+7 = 0; x=-7
Substituting each of the values of x to the equation makes y undefined.
Finding also the oblique asymptotes if needed, one uses the long division process:
\(x - 6\)
\(x^{2} + 16x + 63 \sqrt{ x^{3} + 10x^{2} + 16x +96 }\)
\(-({ x^{3} + 16x^{2} + 63x} )\)
\(-6x^{2} - 47x +96\)
\(-(6x^{2} -96x -378)\)
\(49x+474\)
The oblique asymptote equation is : y=x-6
