Question

x+2/x+1-x+4/x+3=x+6/x+5-x+8/x+7

Answer 1

x+2/x+1-x+4/x+3=x+6/x+5-x+8/x+7
(x+1+1)/(x+1)-(x+3+1)/(x+3)=(x+5+1)/(x+5)-(x+7+1)/(x+7)
(x+1)/(x+1)+1/(x+1)-(x+3)/(x+3)-1/(x+3)=(x+5)/(x+5)+1/(x+5)-(x+7)/(x+7)-1/(x+7)
1+1/(x+1)-1-1/(x+3)=1+1/(x+5)-1-1/(x+7)
1/(x+1)-1/(x+3)=1/(x+5)-1/(x+7)
(x+3)/(x+1)(x+3)-(x+1)/(x+1)(x+3)=(x+7)/(x+5)(x+7)-(x+5)/(x+5)(x+7)
2/(x+1)(x+3)=2/(x+5)(x+7)
(x+1)(x+3)=(x+5)(x+7)
x^2+4x+3=x^2+12x+35
8x=-32
x=-4

Answer 2

(x+2)/(x+1)-(x+4)/(x+3)=(x+6)/(x+5)-(x+8)/(x+7)
(x+1+1)/(x+1)-(x+3+1)/(x+3)=(x+5+1)/(x+5)-(x+7+1)/(x+7)
1+1/(x+1)-1-1/(x+3)=1+1/(x+5)-1-1/(x+7)
1/(x+1)-1/(x+3)=1/(x+5)-1/(x+7)
1/(x+1)+1/(x+7)=1/(x+3)+1/(x+5)
(x+7+x+1)/[(x+1)(x+7)]=(x+3+x+5)/[(x+3)(x+5)]
(2x+8)/(x^2+8x+7)=(2x+8)/(x^2+8x+15)
(2x+8)*[1/(x^2+8x+7)-1/(x^2+8x+15)]=0
因为x^2+8x+7不等于x^2+8x+15
所以1/(x^2+8x+7)-1/(x^2+8x+15)不等于0
所以2x+8=0
x=-4