一道初中数学题求解

1/（x-2）+k/(x+2)=3/(x^-4)
[k(x-2)+(x+2)]/(x^-4)=3/(x^-4)
[(k+1)x+2(1-k)]/(x^-4)=3/(x^-4)
[(k+1)x+2(1-k)]=3
(k+1)x=2k+1
x=(2k+1)/(k+1),有增根，则增根为±2
→(2k+1)/(k+1)=2(无解),或(2k+1)/(k+1)=-2→k=-3/4
∴当k=-3/4时,关于x的分式方程 1/（x-2）+k/(x+2)=3/(x^-4)有增根，则增根为-2