Question

化简求值（1/x+1+1/x-1）*x^2+2x-3/x^2+3x，其中x=√3

Answer 1

1/(x+1)+1/(x-1)*(x^2+2x-3)/(x^2+3x)
=1/(x+1)+1/(x-1)*(x+3)(x-1)/x(x+3)
=1/(x+1)+1/x
=1/(√3+1)+1/√3
=(√3-1)/(√3+1)(√3-1)+√3/3
=(√3-1)/2+√3/3
=√3/2+√3/3-1/2
=5√3/6-1/2

追问

你确定，你化简错了

追答

应该是这样的：

[1/(x+1)+1/(x-1)]*(x^2+2x-3)/(x^2+3x)
=[1/(x+1)+1/(x-1)]*(x+3)(x-1)/x(x+3)
=[(x-1)/(x+1)(x-1)+(x+1)/(x+1)(x-1)]*(x+3)(x-1)/x(x+3)
=[(x-1+x+1)/(x+1)(x-1)]*(x+3)(x-1)/x(x+3)
=2x/(x+1)(x-1)*(x+3)(x-1)/x(x+3)
=2/(x+1)
=2/(√3+1)
=2(√3-1)/(√3+1)(√3-1)
=√3-1

追问

很好