 So in general, if we have a rational equation, we can transform it into a polynomial equation by multiplying by the denominators. But, remember, any values that were forbidden before cannot be permitted as solution values. So if we have something like this, we see that the forbidden values are x equal to 1 and x equal to 3. So our denominators are x minus 1 and 3 minus x. So if we multiply through by x minus 1 we get, and we still have the denominator 3 minus x. So we'll multiply all of our terms by 3 minus x and simplify. Now this is something of a mess, so let's expand and collect like terms. And we'll note that this is a quadratic equation, so we'll get all of the terms onto one side of the equation. So let's solve this quadratic. Notice that every term has a common factor of 4, so let's go ahead and remove that common factor. And since 4 is not equal to 0, unless you're a politician responding to allegations of misconduct, we can divide both sides by 4 and we get this thing that we have to factor. And after a considerable amount of effort, we find it does factor as, and so we have product equal to 0 and so 1 or the other factor must be 0. So either 5x minus 11 is 0 and we solve that to get, or x minus 2 equals 0 and we solve that to get. And so we have our two solutions. Neither of these are forbidden values, so both are solutions. It's important to remember that a forbidden value can never be a solution. So when we have an equation involving rational expressions, we should always start by finding the forbidden values. If we multiply through by the product of the denominators c minus 9 times c minus 5 we get, maybe simplify a little more, and since we have a quadratic equation, we'll get all the terms onto one side, and then try to solve, in this case we'll attempt a factor, and so we have product of two things equal to 0 and so our solutions are going to be. But remember, a forbidden value can never be a solution, and c equals 9 is one of our forbidden values, so this is not a solution. And in fact the only solution is going to be c equals negative 5.