Question

先化简再求值 x²-2x/x÷(x-4/x) 其中x=3

(1+1/x-2)÷x²-2x+1/x²-4 其中x=-5
[1+2x-4/(x+1)(x-2)]÷x+3/x²-1 其中x=6
跪求啊...

Answer 1

x²-2x/x÷(x-4/x)
=x(x-2)/x×x/(x+2)(x-2)
=x/(x+2)
当x=3时 原式=3/(3+2)=3/5

(1+1/x-2)÷x²-2x+1/x²-4
=(x-1)/(x-2)×(x+2)(x-2)/(x-1)²
=(x+2)/(x-1)
当x=-5时
原式=-3/(-6)=1/2

[1+2x-4/(x+1)(x-2)]÷x+3/x²-1
=(x+3)/(x+1)×(x+1)(x-1)/(x+3)
=x-1
当x=6时
原式=6-1=5

Answer 2

(x²-2x)/x÷(x-4/x) 其中x=3

(x-2)÷((x²-4)/x)
=(x-2)x/((x+2)(x-2))
=x/(x+2)
=3/(3+2)
=3/5
(1+1/(x-2))÷((x²-2x+1)/(x²-4)) 其中x=-5
=(x-2+1)/(x-2)÷((x-1)²/((x+2)(x-2)))
=(x-1)/(x-2)*(x-2)(x+2)/(x-1)²
=(x+2)/(x-1)
=(-5+2)/(-5-1)
=(-3)/(-6)
=1/2
[1+(2x-4)/((x+1)(x-2))]÷((x+3)/(x²-1)) 其中x=6
=(1+2(x-2)/((x+1)(x-2)))*(x+1)(x-1)/(x+3)
=(1+2/(x+1))*(x+1)(x-1)/(x+3)
=(x+1+2)/(x+1)*(x+1)(x-1)/(x+3)
=(x+3)/(x+1)*(x+1)(x-1)/(x+3)
=x-1
=6-1
=5