 In this video, we present the solution to question number eight from practice exam number three for math 1050. We're given a rational function f of x in factored form. It's 3x minus 1 times 2x plus 7 over x plus 2 times 5x plus 4. We're asked to find the domain of this function. Well, when it comes to the domain of a rational function, the only thing that we have to worry about is dividing by 0. So whatever happens in the numerator doesn't matter whatsoever. We can just ignore it like so. Even if there was a common factor in the numerator that cancels with one of the denominator, the domain is always computed from the original formula, not some simplified version of that. So what makes the denominator go to 0? Well, if you set the denominator equal to 0, this is a factored quadratic equation. We set each factor equal to 0 and solve for it. And so from the first factor, we see that x should not equal negative 2. From the second factor, we see that x should not be negative 4 over 5, which actually I'm writing over the right answer. This would then tell us that the correct answer is then b, all real numbers except for negative 2 and negative 4 fifths.