Expert: Richard J. Raridon - 5/3/2010

Question
Hi, Richard. Quite some time has gone by since my last algebra course and, naturally, I don't remember everything I learned in that course. I'm currently enrolled in a physics course and haven't had any issues with the algebra of it until now. I want to isolate "H" from the following equation, but have no idea how to.

(n_1)(W/sqrt(H^2+W^2))=(n_2)(W/sqrt(W^2+4H^2))

What is confusing me most is what to do when we have a square root in the denominator of a fraction. If you could help me figure this one out, that would be wonderful. Thank you in advance for your time and expertise, Ariel

Answer
First of all, you can write sqrt(H^2+W^2) as (H^2+W^2)^1/2
When you have that in the denominator you want to multiply top and bottom by (H^2-W^2)^1/2
so you get (H^2-W^2)^1/2/(H^4-W^4)
For the other one you want to multiply by (W^2-4H^2)^1/2 to get (W^2-4H^2)^1/2/(W^4-16H^4)
I don't know what you mean by n_1 and n_2 so I can't complete the problem for you but maybe you can take it from there.