Simplifying 1/(√3+1) + (√3+1)²

[Skeletor]

HELP! PLease cna someone explain how to do this quck please?!

1
----- + (root3+1)squared
root3+1

 

[Icebreaker]

What are you trying to find?

 

[Moo Of Doom]

$$\frac{1}{\sqrt{3}+1}+(\sqrt{3}+1)^2$$
is I believe what he was trying to get the answer to.

EDIT: Bah, read below...

 

[Oggy]

I got $$\frac{5}{2}\sqrt{3}+\frac{7}{2}$$

 

[Moo Of Doom]

What? Wait... d'oh! I forgot to divide the other half of the expression by $$\sqrt{3}-1$$... Seems like the whole thing doesn't work now...

Then you have to go about it like so:

$$\frac{1}{\sqrt{3}+1}+(\sqrt{3}+1)^2$$
$$=\frac{1+(\sqrt{3}+1)^3}{\sqrt{3}+1}$$
$$=\frac{(1+(\sqrt{3}+1)^3)(\sqrt{3}-1)}{(\sqrt{3}+1)(\sqrt{3}-1)}$$
$$=\frac{\sqrt{3}-1+2(\sqrt{3}+1)^2}{2}$$
$$=\frac{\sqrt{3}-1+4\sqrt{3}+8}{2}$$
$$=\frac{5\sqrt{3}+7}{2}$$
$$=\frac{5}{2}\sqrt{3}+\frac{7}{2}$$

Which is far more correct...