 Well, how about those radicals? Let's take a look at our difference quotient for radical functions, and let's take a nice simple one, f of x equals square root of 3x minus 1. Again, our difference quotient always has the same form, it's f of x plus h minus f of x all over h. So again, we want to find f of x and f of x plus h, so f of x, well there it is, square root of 3x minus 1, we'll go ahead and write that down, f of x plus h, again we can start out by just dropping out our x variables and leaving an empty set of parentheses in their place, f of blank is 3 blank minus 1, and whatever I put in the 1, I want to put in all of them. So I would like to put in an x plus h in the first set of parentheses, that x plus h has to go in all those sets of parentheses, and I end up with that, and maybe a little bit of expansion will make our lives easier, expanding that out 3x plus 3h minus 1. And we can go ahead and set up our difference quotient. So let's take a look at that, that'll be again, f of x plus h minus f of x, here's f of x plus h, here's f of x, all divided by h. And so there's our set up for the difference quotient, and let's see, that's a square root minus a square root. So one nice way we have of simplifying an expression like that is we can try to rationalize the numerator. So I'll multiply by the conjugate. Again, remember the conjugate is the same terms, this time we're going to change the sign. So it used to be minus, now it's plus. But the terms themselves are exactly the same. And because I don't want to change the actual value of the expression, I'm going to divide by the same thing that I'm multiplying by. So let's take a look at that. And I'll multiply those expressions together. Again, the value of multiplying by the conjugate is I get first one squared minus second one squared. Again, as before, I can leave the denominator in factored form h times this mess. And the reason is maybe I don't need to do any simplification of the denominator. So let's see what happens if I square both of the square root terms. I get 3x plus 3h minus 1 and 3x minus 1, expanding that out a little further. Again, don't forget that minus applies to everything in that 3x minus 1. I get this and oh, good. A bunch of things cancel out. There's a 3x minus 3x. There's a minus 1 plus 1. All of those things go away. We're left with 3h. And once again, there's an h in the numerator, h in the denominator. And I can cancel them as long as I add in the qualifier that says h cannot be equal to 0. So I'll go ahead and do that. And there's my simplified form of the difference quotient for this radical function.