x²+x+1/4x²-1 > 1
x²+x+1/4x²-1 -1 > 0
x²+x+1-(4x²-1) / 4x²-1 > 0
x²+x+1-4x²+1 / 4x²-1 >0
-3x² +3x-2x+2/4x²-1 > 0
-3x (x-1) - 2(x-1)/4x²-1 > 0
-(-x-1)(3x+2) / 4x2-1 >0