关于x的方程x/(x+1)-(x+1)/(x-1)=a/x^-1的解是正数,则a必须满足的条件是什么

Answer 1

x/(x+1)-(x+1)/(x-1)=a/(x^2-1)
两边乘以(x+1)(x-1),得
x(x-1)-(x+1)²=a
x²-x-x²-2x-1=a
-3x=1+a
x=-(1+a)/3
要正数-(1+a)/3>0
-(1+a)>0
a