Question

已知y=x²-x 分之x 除以x²-2x+1 分之 x²-1 减去 x+1分之2 ，当x为何值时。y的值为3分之1

Answer 1

解：
y=[x/(x²-x)]÷[(x²-1)/(x²-2x+1)]-[2/(x+1)]
={x/[x(x-1)]÷[(x-1)(x+1)/(x-1)²]-[2/(x+1)]
=[1/(x-1)]÷[(x+1)/(x-1)]-[2/(x+1)]
=[1/(x-1)]×[(x-1)/(x+1)]-[2/(x+1)]
=[1/(x+1)]-[2/(x+1)]
=-1/(x+1)
∵ y=1/3
∴ -1/(x+1)=1/3
∴ x+1=-3
∴ x=-4
∴ 当x=-4时，y的值为1/3

Answer 2

x=-4

追问

说下过程啊！！！

追答

将原式约分一下简化，分解因式简化，如x^2-2x+1可分解为(x-1)^2，x^2-1可分解为(x+1)(x-1)等