方程(a-x²)/(a-x)²-1/a=(a-1)/[a³-ax(2a-x)]的正整数解x为_________.当解为正整数时,a应

方程(a-x²)/(a-x)²-1/a=(a-1)/[a³-ax(2a-x)]的正整数解x为_________.当解为正整数时,a应
方程(a-x²)/(a-x)²-1/a=(a-1)/[a³-ax(2a-x)]的正整数解x为_________.当解为正整数时,a应

方程(a-x²)/(a-x)²-1/a=(a-1)/[a³-ax(2a-x)]的正整数解x为_________.当解为正整数时,a应
[a³-ax(2a-x)]=a(a-x)²
方程化为：a(a-x²)-(a-x)²=a-1
即-(x-1)²a=x²-1=(x-1)(x+1)------>x=1或-(x-1)a=x+1
x=1或x=(a-1)/(a+1)
x=1.a=(1+x)/(1-x)