Show that the function is a solution of the wave equation

[robertmatthew]

Homework Statement

Show that the function is a solution of the wave equation u_tt = a²u_xx.

u = (t)/(a²t²-x²)

Homework Equations

Quotient rule
(f/g)' = (g*f ' - f*g') / g²

The Attempt at a Solution

I began with the first and second partials of u with respect to x:
http://imageshack.com/a/img661/7646/Xnbsd2.png
I'm fairly confident that this part is correct, because I checked it with an online calculator.
Then I did the first partial of u with respect to t:
http://imageshack.com/a/img537/4254/5hYVrv.png
Then the second partial:
http://imageshack.com/a/img537/7426/Xr15AC.png So I'm getting -u_tt = a²u_xx. I've done this several times now, and I keep getting the extra negative sign in u_tt. I can't figure out where it's coming from; I'm sure it's some silly mistake with a dropped sign somewhere. I'd appreciate the help of anyone who could help me spot it.

 

[RUber]

*Edit* Sorry I misspoke on the initial response.
It looks like in your simplification of the second partial wrt t, you cancel a negative sign incorrectly.

 

[robertmatthew]

Ah, I see it now. No idea why I kept thinking I could do that; I must have done this problem five or six times and did that every time. Thanks for your help!