Question

﹙x＋2﹚／﹙x＋1﹚－﹙x＋3﹚／﹙x＋2﹚=﹙x＋4﹚／﹙x＋3﹚－﹙x＋5﹚／﹙x＋4﹚详细简便！！！！！！

Answer 1

先看其中的一项
(x+2)/(x+1)=[(x+1)+1]/(x+1)=(x+1)/(x+1)+1/(x+1)=1+1/(x+1)

其余一样
1+1/(x+1)-1-1/(x+2)=1+1/(x+3)-1/(x+4)
1/(x+1)-1/(x+2)=1/(x+3)-1/(x+4)
[(x+2)-(x+1)]/(x+1)(x+2)=[(x+4)-(x+3)]/(x+3)(x+4)
1/(x+1)(x+2)=1/(x+3)(x+4)
(x+3)(x+4)=(x+1)(x+2)
x²+7x+12=x²+3x+2
4x=-10
x=-5/2
检验：

Answer 2

(x+2) / (x+1) = [(x+1)+1] / (x+1) = 1 + 1 / (x+1)
﹙x＋2﹚／﹙x＋1﹚－﹙x＋3﹚／﹙x＋2﹚=﹙x＋4﹚／﹙x＋3﹚－﹙x＋5﹚／﹙x＋4﹚
==> 1 + 1/(x+1) - 1 - 1/(x+2) = 1 + 1/(x+3) - 1 - 1/(x+4)
==> 1/(x+1) - 1/(x+2) = 1/(x+3) - 1/(x+4)
==> 1/[(x+1)(x+2)] = 1/[(x+3)(x+4)]
==>(x+1)(x+2)=(x+3)(x+4)
==>x²+3x+2=x²+7x+12
==>x=-5/2
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