Question

x+1/x-1+4/x²-1=1怎么解？？

Answer 1

x+1/x-1+4/x²-1=1
解：两边同时乘以(x²-1)得：
(x+1)²+4=x²-1
去括号，移项，合并同类项得：
2x=-6
x=-3

Answer 2

x+1/x-1+4/x²-1=1
(x+1)/(x-1)+4/(x+1)(x-1)=1等式两边同乘(x+1)(x-1)
(x+1)^2+4=(x+1)(x-1)
x^2+2x+1+4=x^2-1
2x=-6
x=-3

不懂可追问
满意请采纳
谢谢

追问

还有道题，(1/x-2-1/x+1)× x²-1/3，其中x=3

追答

(1/x-2-1/x+1)× x²-1/3
=(x+1-(x-2))/(x+1)(x-2)-1/3
=(x+1-x+2)/(x+1)(x-2)-1/3
=3/(x+1)(x-2)-1/3
=(9-(x+1)(x-2))/3(x+1)(x-2)
=(9-x^2+x+2)/3(x+1)(x-2)
=(-x^2+x+11)/3(x+1)(x-2)
=(-3^2+3+11)/3(3+1)(3-2)
=(-9+3+11)/(3*4*1)
=5/12

追问

谢了

追答

(1/x-2-1/x+1)× x²-1/3
=x^2(x+1-x+2)/(x+1)(x-2)-1/3
=3x^2/(x+1)(x-2)-1/3
=(9x^2-(x+1)(x-2))/3(x+1)(x-2)
=(9x^2-x^2+x+2)/3(x+1)(x-2)
=(8x^2+x+2)/3(x+1)(x-2)3
=(8*3^2+3+2)/3(3+1)(3-2)
=(72+3+2)/(3*4*1)
=77/12

Answer 3

两边乘(x+1)(x-1)
(x+1)²+4=(x+1)(x-1)
x²+2x+1+4=x²-1
2x+5=-1
x=-3
经检验，x=-3是方程的解