How do you find the excluded value if there is another variable or number in the denominator? Such as the equation 12(a) over a squared minus 3(a) minus 10?

Answer 1

12 a /(a^2 -3 a -10)

if the denominator is zero, that is undefined and out of the domain
so all we want to know is for what a is the denominator zero. It does not matter what the numerator is

a^2 -3 a -10 = 0

a = [ 3 +/- sqrt (9 +40) ]/2

a = 10/2 or -4/2
so
a = 5 or -2 are EXCLUDED from our domain