Sorry if this seems like a dumb question, or if it has been answered already. I did a quick search and didn't turn up anything, so here goes.
I'm teaching a high school algebra class, and the book I'm doing says the students need to note restrictions on both the numerator and denominator when dividing two polynomials. For example:
$$\frac{ \left(\frac{x^2-121}{x^2-4} \right)}{ \left(\frac{x+2}{x-11} \right)}$$
There is obviously going to be an asymptote at $x = -2$, but the book also suggests there should be a hole in the graph at $x = 11$.
However, graphing the function on a graphing calculator (desmos, in this case), shows the function to be equal to $0$ when $x = 11$. Changing the numerator of the dividend to something like $(x² - 133)$ doesn't alter the equation equaling zero at $x = 11$ either.
Wouldn't $x = 11$ imply that $(x² - 133)/(x² - 4) ÷ (x+2)/(x-11)$ is actually $(x² - 133)/(x² - 4) ÷ 1/0$, or $(x² - 133)/(x² - 4) ÷ ∞$?
Note: the TI-83 also gives me an ERROR message for this function at $x = 11$, so perhaps it is just desmos?
Edit: Sorry! I forgot to include another division sign when discussing this problem.