Question

(x+1)/(x+2)+(x+8)/(x+9)=(x+2)/(x+3)+(x+7)/(x+8) 起价5分 看谁的简单

Answer 1

(x+1)/(x+2)+(x+8)/(x+9)=(x+2)/(x+3)+(x+7)/(x+8)
(x+2-1)/(x+2)+(x+9-1)/(x+9)=(x+3-1)/(x+3)+(x+8-1)/(x+8)
1-1/(x+2)+1-1/(x+9)=1-1/(x+3)+1-1/(x+8)
-1/(x+2)-1/(x+9)=-1/(x+3)-1/(x+8)
1/(x+2)-1/(x+3)=1/(x+8) -1/(x+9)
(x+3)/(x+2)(x+3)-(x+2)/(x+2)(x+3)=(x+9)/(x+8)(x+9) -(x+8)/(x+8)(x+9)
[(x+3)-(x+2)]/(x+2)(x+3)=[(x+9) -(x+8)]/(x+8)(x+9)
1/(x+2)(x+3)=1/(x+8)(x+9)
(x+2)(x+3)=(x+8)(x+9)
x^2+5x+6=x^2+17x+72
17x-5x=72-6
12x=66
2x=11
x=11/2
经检验x=11/2是方程的解

Answer 2

(x+1)/(x+2)+(x+8)/(x+9)=(x+2)/(x+3)+(x+7)/(x+8)
1-1/(x+2)+1-1/(x+9)=1-1/(x+3)+1-1/(x+8)
1/(x+2)+1/(x+9)=1/(x+3)+1/(x+8)
1/(x+2)-1/(x+3)=1/(x+8)-1/(x+9)
1/(x+2)(x+3)=1/(x+8)(x+9)
(x+8)(x+9)=(x+2)(x+3)
x²+17x+72=x²+5x+6
12x=-66
x=-5.5

Answer 3

等价于 1/x+2+1/x+9=1/x+3+1/x+8
等价于 1/x+2-1/x+3=1/x+8-1/x+9
即 1/(x+2)(x+3)=1/(x+8)(x+9)
即(x+2)(x+3)=(x+8)(x+9)
化简得 x=-11/2

Answer 4

(x+1)/(x+2)+(x+8)/(x+9)=(x+2)/(x+3)+(x+7)/(x+8)
1/(x+2)-1+1/(x+9)-1=1/(x+3)-1+1/(x+8)-1
1/(x+2)+1/(x+9)=1/(x+3)+1/(x+8)
1/（x+2)-1/(x+3)=1/(x+8)-1/(x+9)
1/[(x+2)(x+3)]=1/[(x+8)(x+9)]
(x+2)(x+3)=(x+8)(x+9)
x^2+5x+6=x^2+17x+72
12x=-66
x=-5.5

追问

还没看懂啊