Question 6182
When we've got variables in the denominator, things get risky. There are certain troublemaker values for variables in the denominator that make the entire denominator equal to zero - that, we can't have in math.


So let's take just the denominator: {{{ b^2 - 2b - 8 }}}. We know that it's factorable to {{{ (b - 4)(b + 2) }}}. Now, we DON'T want b to be values that will make that denominator zero. The thing is, we must first find the troublemaker values for b. So, what values of b will make the denominator zero? 


{{{ (b - 4)(b + 2) = 0 }}} <---- Just by looking at this equation, b = 4 or b = -2 are the two values that will make the denominator zero. In other words, the fraction fails if b = 4 or -2. SO, the legal values for b is the set of all real numbers EXCEPT 4 and -2. AKA, anything, as long as it's not 4 or -2.