 So let's multiply these two rational functions. So r of x is f of x times g of x, and so equals means replaceable. We'll replace f of x with what it's equal to, and we'll replace g of x with what it's equal to. Now if we wanted to simplify this mess, what we'll try and do is we'll try and factor and remove common factors. And looking at all of these things, we might guess that x squared plus 10x plus 16 is probably the easiest to factor because all of the terms are positive, which means you don't have to mess around with signs. And so we'll start by finding all numbers that multiply to 16. And remember, the only way to see if a factorization works is to check to see if it works. So we'll start off with this first pair, 1 and 16. Maybe we're really lucky and x squared plus 10x plus 16 is x plus 1 times x plus 16. But I wouldn't count on it, so let's go ahead and multiply it out and see if this factorization is correct. And it isn't. So we'll move on to the next 2 and 8. Is x squared plus 10x plus 16 equal to x plus 2 times x plus 8? And this time we got lucky, it is. And so that starts our factorization. Now remember, factorization is the hardest, easy problem in mathematics. And so any help we can get is going to be useful. And so it helps to remember a factor only matters if it's a common factor. And so at this point, we have 2 factors, x plus 2 and x plus 8. And we can see if either of these is a factor of the numerator, x squared minus 16x plus 64. So is x squared minus 16x plus 64 x plus 2 times something? Well, since our constant term is positive 64, our something has to be x plus 32. So we'll check it. And no. But maybe it's x plus 8 times something. Well, if it is, that something has to be x plus 8. So we'll check it out. And be very disappointed. But we do have another possibility. x squared plus 7x minus 8 is going to be in the numerator. So let's see if either x plus 2 or x plus 8 is a factor. So maybe x plus 2 is a factor, in which case the other factor has to be x minus 4 and maybe... Nope. But let's check x plus 8. Is x squared plus 7x minus 8 equal to x plus 8 times something? If it is, the something has to be x minus 1. And brace yourself for disappointment because we find out that... Oh, hey, it works. And so there's our factorization of x squared plus 7x minus 8. Well, now we have a new factor in the numerator, x minus 1. So let's see if x minus 1 is a factor of the remaining term in the denominator, x squared minus 6x minus 16. Can we write x squared minus 6x minus 16 as x minus 1 times something? Well, our something would have to be x plus 16. And we check it out and we find... Nope. And unfortunately, this leaves us with two things, x squared minus 16x plus 64 and x squared minus 6x minus 16, which are potentially factorable. And so we still have to factor. And we can take our choice and let's try to factor x squared minus 6x minus 16. And so we need numbers that multiply to minus 16, which are... And we have to try them out one by one. So we'll try 1 and negative 16. Does x squared minus 6x minus 16 factor as x plus 1 times x minus 16? Nope. But how about x plus 2 times x minus 8? And success! So again, a factor only matters if it's a common factor. Now, we've already checked to see if x plus 2 is a factor of x squared minus 16x plus 64. So we'll only need to check to see if x minus 8 is a factor. So we'll see if x squared minus 16x plus 64 factors as x minus 8 times something and are something, in order to get this plus 64 has to be another x minus 8. And so we'll check and it works. So now we can remove those common factors and what's left is x minus 1 times x minus 8 over x plus 2 times x plus 2. Now, in order to enter this expression into my open math, again, the important thing here is to make sure that what you're telling the computer is what you want to be telling the computer. So this is the answer we want and we need to make sure that when we preview the answer we give, it's the same answer. Remember, no computer was ever fired for misentering a number. So if we type this in, we see the preview and since the preview is exactly what we want, oh wait, it isn't. Which means if we hit submit, the answer that we're actually submitting is this and not the answer we want to submit. And so the easiest way to fix that is to remember that whenever you enter in a fraction, it helps to put the entire numerator and the entire denominator inside a set of parentheses. Again, even though the syntax is fine, this is not the answer we want. We need to make sure the denominator is also in a set of parentheses. And now what we've answered is what we wanted to answer, so now we're ready to hit submit and get our score.