Verify that u = t /(a^2 t^2 - x^2) satisfies the wave equation utt = a^2 uxx (Subscript tt and xx)

I've tried many different ways in deriving this...can't seem to get the answer! I tried the quotient rule, but it didn't work...I just tried the product rule by bringing up the denominator as (a^2 t^2 - x^2)^-1 but I get an x that I cannot get rid of!

Help would be appreciated!