如果分式方程x+1x=c+1c的两根为x1=c，x2=1c，那么y+1y-1=m+1m-1的两个根为y1=m，y2=．

Question

如果分式方程x+ (1)/(x)=c+ (1)/(c)的两根为x₁=c，x₂= (1)/(c)，那么y+ (1)/(y-1)=m+ (1)/(m-1)的两个根为y₁=m，y₂=___．

Answer 1

y+(1)/(y-1)=m+(1)/(m-1)变形为y-1+(1)/(y-1)=m-1+(1)/(m-1)，
∵分式方程x+(1)/(x)=c+(1)/(c)的两根为x₁=c，x₂=(1)/(c)，
∴y+(1)/(y-1)=m+(1)/(m-1)的两个根为y₁-1=m-1，y₂-1=(1)/(m-1)，
∴y₁=m，y₂=(m)/(m-1)，
故答案为：y₂=(m)/(m-1)．