Question

(x+1/x+2)+(x+2/x+3)=(x+3/x+4)+(x+4/x+5)

Answer 1

(x+2-1)/(x+2)+(x+3-1)/(x+3)=(x+4-1)/(x+4)+(x+5-1)/(x+5)
1-1/(x+2)+1-1/(x+3)=1-1/(x+4)+1-1/(x+5)
1/(x+2)-1/(x+4)=1/(x+5)-1/(x+3)
2/(x²+6x+8)=-2/(x²+8x+15)
x²+8x+15=-x²-6x-8
2x²+14x+23=0
x=(-14±2√3)/4=(-7±√3)/2
经检验，x=(-7±√3)/2是方程的根

Answer 2

x+2/x+1-x+3/x+2=x+4/x+3-x+5/x+4
(x+2)(x+2)/(x+1)(x+2)-(x+3)(x+1)/(x+1)(x+2)=(x+4)(x+4)/(x+4)(x+3)-(x+5)(x+3)/(x+3)(x+4)
[(x+2)^2-(x+3)(x+1)]/(x+2)(x+1)=[(x+4)^2-(x+3)(x+5)]/(x+3)(x+4)
1/(x+2)(x+1)=1/(x+3)(x+5)
(x+2)(x+1)=(x+3)(x+5)
x^2+3x+2=x^2+8x+15
3x+2=8x+15
5x=-13
x=-13/5

Answer 3

(x+1/x+2)+(x+2/x+3)=(x+3/x+4)+(x+4/x+5)
4/x+5=0
x=4/5