For example, consider the rational expression 3x/(x^2 – 16). What values in the denominator must we be mindful of? Explain why???

What is the main danger you can encounter in the denominator? What is the 1 value you absolutely cannot have? Thats right, zero. your denominator cant be zero and still have a continuous function.

So your equation in particular, you need to concentrate on what values of x will give a value of zero in the denominator. You can use the quadratic formula or you can factor the polynomial. either way you will find that the denominator will be zero when
x= 4 and -4.