Question

先化简再求值:x2-1/x2-2x+1 +x2-2x/x-2 ÷x,其中x=2/3

Answer 1

(x^2-1)/(x^2-2x+1) +(x^2-2x)/(x-2) ÷x
=(x-1)(x+1)/(x-1)^2+x(x-2)/(x-2) *1/x
=(x+1)/(x-1)+1
=(x+1+x-1)/(x-1)
=2x/(x-1)
=(2*2/3)/(2/3-1)
=(4/3)/(-1/3)
=-4/3*3
=-4

追问

当x为何值时，下列分式有意义？（要过程）x+1/1-x，2x/（1-x）2，ax/x

追答

(x+1)/(1-x)
当x≠1时，分式有意义

2x/(1-x)^2
当x≠1时，分式有意义

ax/x
当x≠0时，分式有意义

追问

计算（要过程）：1/x-1/x+1。化简:2/a^2-1 - 1/a-1，x/x-1*(1- x-1/x)，x+2/x^2-2x-1/x-2)÷2/x，
1/x+1-x+2/x^2-1*x^2-2x+1/x^2-4。

Answer 2

x2-1/x2-2x+1 +x2-2x/x-2 ÷x
=(x+1)(x-1)/(x-1)^2+x(x-2)/(x-2)÷x
=(x+1)/(x-1)+1
=2x/(x-1) x=2/3
=(4/3)/(-1/3)
=-4

追问

化简（要过程）： (1+4/a^2-4)*a+2/a ，（x ^2/x+2-4/x+2）÷x-2/x

追答

(1+4/a^2-4)*a+2/a
=a^3/(a^2-4)+2/a
=(a^4+2a^2-8)/a(a^2-4)
（x ^2/x+2-4/x+2）÷x-2/x
=(x^2-4)/(x-2)*x/(x-2)
=(x+2)(x-2)/(x-2)*x/(x-2)=(x+2)x/(x-2)