方程(a-x²)/(a-x)²-1/a=(a-1)/[a³-ax(2a-x)]的正整数解x为_____数学解答

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

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解答

[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+1x=1或x=(a-1)/(a+1)x=1.a=(1+x)/(1-x)