Space Charge width proof using Algebra

[cnafets]

Homework Statement

Use
N_aX_po=N_dX_no
X_po=$$\sqrt{(2\epsilon\phi/qNa)(Nd/(Nd+Na)}$$
X_no=$$\sqrt{(2\epsilon\phi/qNd)(Na/(Nd+Na)}$$
to prove

X_do=X_do+X_no=$$\sqrt{(2\epsilon\phi/q)((1/Nd)+(1/Na))}$$

Homework Equations

(1/Na)+(1/Nd)= (Na+Nd)/(Na)(Nd)

The Attempt at a Solution

I get stuck at:
X²_do=$$(2\epsilon\phi/q(Nd+Na))((Nd/Na)+(Na/Nd))$$
I squared both sides to get rid of the sqrt temporarily, I'll take the sqrt again at the end.
Then I combined like terms and I don't know where to go after that. Someone help :(

 

[cnafets]

The Attempt at a Solution

I get stuck at:
X²_do=$$(2\epsilon\phi/q(Nd+Na))((Nd/Na)+(Na/Nd))$$
I squared both sides to get rid of the sqrt temporarily, I'll take the sqrt again at the end.
Then I combined like terms and I don't know where to go after that. Someone help :(

EDIT:
Now I get

X_do= $${\sqrt{2\epsilon_{s}\phi_{B}/q}\left( \sqrt{\stackrel{N_{d}}{N_{a}(N_{a}+N_{d})}}+\sqrt{\stackrel{N_{a}}{N_{a}(N_{a}+N_{d})}}\right)$$