- #1

- 3,802

- 95

## Homework Statement

Simplify to a certain extent, as much as possible (factorized form would be best):

[tex]\frac{\sqrt{3}}{2}\left(\frac{md}{m-\sqrt{3}}\right)^2+\frac{\sqrt{3}}{2}\left(\frac{m(s+d)}{m+\sqrt{3}}\right)^2+\frac{1}{2}\left(s+\frac{md}{m-\sqrt{3}}-\frac{m(s+d)}{m+\sqrt{3}}\right)\left(\frac{\sqrt{3}md}{\sqrt{3}-m}+\frac{\sqrt{3}m(s+d)}{m+\sqrt{3}}\right)[/tex]

## The Attempt at a Solution

This isn't an actual question but rather a part of a bigger picture. I need this simplified as much as possible before I can even think of manipulating it further.

I've tried quite a bit, but after expanding the last factored expression, it became pretty ugly. This route seems most promising:

[tex]\frac{\sqrt{3}}{2}\left(\left(\frac{md}{m-\sqrt{3}}\right)^2+\left(\frac{m(s+d)}{m+\sqrt{3}}\right)^2+\left(s+\frac{md}{m-\sqrt{3}}-\frac{m(s+d)}{m+\sqrt{3}}\right)\left(\frac{m(s+d)}{m+\sqrt{3}}-\frac{md}{m-\sqrt{3}}\right)\right)[/tex]

[tex]\frac{\sqrt{3}}{2}\left(\left(\frac{md}{m-\sqrt{3}}\right)^2+\left(\frac{m(s+d)}{m+\sqrt{3}}\right)^2+s\left(\frac{m(s+d)}{m+\sqrt{3}}-\frac{md}{m-\sqrt{3}}\right)-\left(\frac{2\sqrt{3}md+\sqrt{3}ms-m^2s}{m^2-3}\right)^2\right)[/tex]

[tex]\frac{\sqrt{3}}{2}\left(\left(\frac{md}{m-\sqrt{3}}\right)^2+\left(\frac{m(s+d)}{m+\sqrt{3}}\right)^2-s\left(\frac{2\sqrt{3}d+\sqrt{3}s-ms}{m^2-3}\right)-m^2\left(\frac{2\sqrt{3}d+\sqrt{3}s-ms}{m^2-3}\right)^2\right)[/tex]

I'm unsure of what else to do without making a big mess. And this still isn't simple enough for what I need this for, so if you have the stomach to tackle this, please do so