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:
[tex] x - 6[/tex]
[tex] x^{2} + 16x + 63 \sqrt{ x^{3} + 10x^{2} + 16x +96 }
[/tex]
[tex]-({ x^{3} + 16x^{2} + 63x} )[/tex]
[tex]-6x^{2} - 47x +96[/tex]
[tex]-(6x^{2} -96x -378)[/tex]
[tex]49x+474[/tex]
The oblique asymptote equation is : y=x-6
