Question

ax$a x^{2} (a+1)+x-a(a-1)=0$

Answer 1

Δ² = 1² + 4 a(a-1)a(a+1) = 1 + 4a²(a² -1 ) = 1 + 4a^4 - 4a²
   = (2a² - 1 )²
so Δ = 2a² -1
x = (-1 + 2a² -1 )/2 a(a+1)      or    x =  (-1 - 2a² +1 )/2a(a+1)
x = (a²-1)/a(a+1)        or  a²/a(a+1)
x  =  (a-1) / a        or  a / (a+1)