Question

解方程：x+1分之x+2-x+3分之x+4=x+5分之x+6-x+7分之x+8

Answer 1

等号前后同时分别计算减法 得：
(x+1)(x+3)分之2=(x+5)(x+7)分之2

所以：
(x+1)(x+3)=(x+5)(x+7)
x^2+4x+3=x^2+12x+35
x=-4

Answer 2

(x+2)/(x+1)-(x+4)/(x+3)=(x+6)/(x+5)-(x+8)/(x+7)
因为(x+2)/(x+1)=1又1/(x+1) 所以方程可以化为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)
2/[(x+1)(x+3)]=2/[(x+5)(x+7)]
x=-4

Answer 3

x+2/x+1=1+1/x+1,同理：原式等于1/(x+1)(x+3）=1/(x+5)(x+7)
(x+5)(x+7)=(x+1)(x+3)
8x=-32
x=-4