Question

计算(x^2+2x+1/x+2)/(x^2-1/x^2+2x)*(x-1/x),并求当x=-3/2时的值

Answer 1

令a=x+1/x
a^2=x^2+2+1/x^2
x^2+1/x^2=a^2-2

所以2a^2-4-3a=1
2a^2-3a-5=0
(2a-5)(a+1)=0
a=5/2,a=-1

x+1/x=5/2
两边乘2x
2x^2-5x+2=0
(2x-1)(x-2)=0
x=1/2,x=2

x+1/x=-1
x^2+x+1=0
无解

x=1/2,x=2

Answer 2

原式=[(x+1)^2/(x+2)]×[x(x+2)/x^2-1)]×[(x^2-1)/x]
=x(x+2)(x+1)^2(x^2-1)/[x(x+2)(x^2-1)]
=(x+1)^2
=(-3/2+1)^2
=1/4