- #1

Kara386

- 208

- 2

## Homework Statement

This is something I need to show in order to solve the question I've been asked. I need to show that

##\sqrt{\frac{N_A}{N_D} } + \sqrt{\frac{N_D}{N_A} } = \frac{N_A + N_B}{\sqrt{N_A N_B}}##

I know these two sides are equal because wolfram alpha says they are, and also because it works if I sub that into my proof. But I'm doing something really really really stupid I think, because I can't get there.

## Homework Equations

## The Attempt at a Solution

I thought it might be easiest to square this and simplify, then square root. So

##(\sqrt{\frac{N_A}{N_D} } + \sqrt{\frac{N_D}{N_A} })^2 = \frac{N_A}{N_D} + 2\sqrt{\frac{N_A N_B}{N_A N_B}} + \frac{N_D}{N_A}##

I suspect that's the step that's wrong but I don't know why. Carrying on anyway:

##= \frac{N_A}{N_D} + \frac{N_D}{N_A} + 2##

Finding a common denominator:

##= \frac{N_A N_D + N_D N_A + 2N_A N_D}{N_A N_D}##

Then finally square rooting again:

##=2##

So that's very different to what I'm after and there is some really awful algebra mistake in there. Unfortunately I can't find it, any help would be very much appreciated! :)