Quotient Rule f(x)=(x+1)/(x-1) Hi everybody! It’s another quotient word problem tonight. This one is really simple: f(x)=(x+1)/(x-1). Let’s go ahead and write out the quotient rule so that we can see the formula that we’re looking at. It’s DX [f(x)/g(x)]=f1(x)g(x)-f(x)g1(x) over [g(x)]2 So, this is the quotient rule and all that means is that we’re taking the derivative, that’s what the D stands for. F(x), I want to talk to you about some of the bottoms, in our case, f(x) is x+1 and g(x) is x-1. In order to take the derivative of this function, we can use this rule and apply this formula. We’ll actually say the derivative of the top times the bottom minus the top times the derivative of the bottom divided by the bottom squared. Let’s go ahead and apply this formula, so we can see what we mean. Well say f1(x) for the derivative and we take the derivative of the top. The derivative of x+1 which is just one times the bottom which is x-1 minus the top x+1 times the derivative of the bottom which the derivative of x-1 is just one, so times one and then we divide by the bottom, x-12. We square because that’s here on the formula. So, we say x-1, getting that from there and then square. Now that we applied the formula, all we need to do is go ahead and simplify this function to get the final answer. Let’s go ahead and distribute the one here. We multiplied one by x-1 and we just get x-1 and then if we distribute the one here, we’ll actually end up with –x and then because we have a negative sign here, a -1 as well. That’s the top and then the bottom. We leave as x-12. This is actually going to turn out to be x-x, so those are going to cancel and then we have -1-1 is actually going to be a -2. So, we’re looking at -2/(x-1)2. That’s actually our final answer. All we need to do was apply the quotient rule to our function to get this function here and then distribute these terms, combine like terms and simplify and this here -2/(x-1)2 is our final answer.