Question

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

Answer 1

(x+2)/(x+1)=1+1/(x+1)

其他分式跟上式类似,可得

1/(x+1)-1/(x+3)=1/(x+5)-1/(x+7)

左右分别计算,

2/(x+1)(x+3)=2/(x+5)(x+7)

即(x+1)(x+3)=(x+5)(x+7)消去x的平方,

4x+3=12x+35

-8x=32

x=-4