# Homework Help: Calculus Question

1. Jul 14, 2010

### physics=death

1. The problem statement, all variables and given/known data

So, I'm trying to review on calculus since I haven't done any in a year and I was skimming the web for problems and I found this. It's got me stumped.

Question:
x
---------------------
[sqrt(x-1)-sqrt(x)]

Solution:
[(2-sqrt(2-x))*(sqrt(x)+sqrt(2-x))]
---------------------------------------
2x-2

That was all that was given. I don't even know how to start this. Anything that would help get me started would be appreciated. :)

2. Relevant equations
Above

3. The attempt at a solution
Well, at first I tried multiplying both sides with sqrt(x-1)+sqrt(x) then simplifying it to see if it matches the solution. But nothing. I'm wondering if the question wants me to find the derivative, integral, I really don't know.

2. Jul 14, 2010

### lanedance

so whats the question? that just look like a few equations to me...

however (try clicking on tex below to see how its written) if you have
$$\frac{x}{\sqrt{x-1} -\sqrt{x}}$$

and want to simplify the usual way is to multiply by the "conjugate" this will remove any root terms from the denominator
$$\frac{x}{\sqrt{x-1} -\sqrt{x}} = \frac{x}{\sqrt{x-1} -\sqrt{x}} \frac{\sqrt{x-1} + \sqrt{x}}{\sqrt{x-1} + \sqrt{x}}$$

so try multiplying out and see where you end up

3. Jul 14, 2010

### Staff: Mentor

Yeah, what's the question? lanedance's suggestion would ordinarily be good advice, but in this case the two expressions (they are not equations) are not equal, so it's not a matter of simplifying, expanding, or manipulating one expression to get the other.

Are you sure you copied the problem correctly? If so, and what you show is all that is given, I would be inclined to not waste any more effort on this problem, and would look elsewhere for problems to do.

4. Jul 14, 2010

### physics=death

Yes, that was my first try but it did not match the solution after simplifying. It's okay, I have already moved on to other problems and have been doing fine.

Those are the only pieces of information given which I agree is a bit shallow in terms of explaining the problem. Anyways, you're right. I have practiced other problems with no other difficulty.

==============

Since the question posted really does not state what the problem is, I cannot really tell what or how to solve.

I apologize if I wasted anyone's time, I have OCD when I cannot figure something out. >_<