12/4x^2+1=-1-(2x+3)/2x
同时乘以4x^2,得
12+4x^2=-4x^2-2x(2x+3)
12+4x^2=-4x^2-4x^2-6x
12+4x^2=-8x^2-6x
12+4x^2+8x^2+6x=0
12x^2+6x+12=0
2x^2+x+2=0
∵△=1-4×2×2=-15＜0
∴原方程无解