1/x-2+k/x+2=4/x²-4 (x+2+kx-2k)/(x²-4)=4/(x²-4) x+kx=4-2+2k x=(2+2k)/(1+k) ∵关于x的分式方程1/x-2+k/x+2=4/x²-4有增根x=2 ∴2=(2+2k)/(1+k) 2+2k=2+2k恒成立 k可取任意值
