Reducing a mathematical expression

[ralden]

Hi guys i need your help!

How can i reduce this equation:

(Nd-Na)*[B*sqrt((Nd-Na)^2) + n^2) - sqrt((Na-Nd)^2) + n^2)]

into this:
(B-1)*(Nd-Na) + (B+1)*sqrt(Nd-Na)^2) + n^2)?

I'm totally depressed, I'm always stocked in sqrt part of the equation:
if there's a techniques in dealing this kind of equation please let me know. thanks.

 

[Mark44]

Hi guys i need your help!

How can i reduce this equation:

(Nd-Na)*[B*sqrt((Nd-Na)^2) + n^2) - sqrt((Na-Nd)^2) + n^2)]

into this:
(B-1)*(Nd-Na) + (B+1)*sqrt(Nd-Na)^2) + n^2)?

Neither of these is an equation (there's no = in either).
Beyond that I don't think you can manipulate the first expression into the second.

$(N_d - N_a) \left[B(\sqrt{(N_d - N_a)^2 + n^2} - \sqrt{(N_a - N_d)^2 + n^2}\right]$
$= (N_d - N_a) \sqrt{(N_d - N_a)^2 + n^2} (B - 1)$

I don't see any obvious way to turn the above into what you're supposed to get. It's possible you have a mistake in what you show for the first expression above.

Note that $(N_a - N_d)^2 = (N_d - N_a)^2$, so the first radical in the original expression is equal to the second radical.

I'm totally depressed, I'm always stocked in sqrt part of the equation:

Don't you mean you're always stuck?

if there's a techniques in dealing this kind of equation please let me know. thanks.

 

[FactChecker]

There are unmatched parenthesis in both expressions. You should check that. Depending on the parenthesis inside the sqrt, the sqrt may disappear. Multiply both expressions out and see it the individual terms match up. If the sqrt didn't disappear, leave it unchanged. If the terms don't match, the expressions are not identical.