 So we can simplify a rational expression any time we can remove common factors from numerator and denominator. Unfortunately, this means we'll actually have to factor. Fortunately, we can do things that will make our life easier, and one of those things is to start with the simple things. And so here we have a polynomial as numerator, a polynomial as denominator. We know we need to factor, but we might notice that b squared minus 9 is a difference of squares. And since b squared minus 9 is a difference of squares, it's easy to factor. And a useful thing to keep in mind is that a factor only matters if it's a common factor. And so our denominator factors as b minus 3 times b plus 3, and so we see if b minus 3 or b plus 3 is a factor of the numerator b squared plus b minus 6. So can we write b squared plus b minus 6 as b minus 3 times something? So let's think about this. Our first terms have to multiply out to b squared. If one of them is b, the other one has to be b as well. Our last terms have to multiply out to minus 6, and that means if one of our constants is minus 3, the other constant has to be plus 2. And that means b squared plus b minus 6 could only be b minus 3 times b plus 2. Or is it? Remember, if you're not willing to put $20 on the table that this is correct, I would check it out. What happens when we multiply b minus 3 times b plus 2? Do we actually get b squared plus b minus 6? And the answer is? And what that means is that this is not a factorization of b squared plus b minus 6. But all hope is not lost. There is a second possibility for the factor b plus 3. And so the question you got to ask yourself is, self, is b squared plus b minus 6 equal to b plus 3 times something? And again, whatever that something is, it has to be a b because we need to get a b squared and a minus 2 because we need to get a minus 6. And again, unless you're willing to throw $20 on the table to say that this is correct, you might want to check it out. So if we multiply b plus 3 times b minus 2, we get which is exactly what we hope to get. And so this is our factorization. Well, now we have factored numerator and denominator. We could remove any common factors that we see and we see this b plus 3 is in both numerator and denominator, so we could remove it, leaving, and at this point we have to enter in our answer. And again, the computer is very, very stupid. It is not able to think it can only do exactly what you tell it to do. So when we enter our answer, we'll want to make sure that it understands we're telling it b minus 2 over b minus 3. If we type this, it gives us a syntax error, which means it doesn't understand us. Well, again, we entered an answer with variable x, but it actually wants an answer with variable b. And it says the syntax is okay, but what it's hearing is this and what we wanted to enter is this. And remember when trying to enter a rational expression or a fraction, we need to enter both numerator and denominator inside a set of parentheses.