Question

x+2分之x+1+(x+7分之x+6)= x+3分之x+2 +(x+6分之x+5)

急
简便方法！！！

Answer 1

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

1/(x+2)+1/(x+7)=1/(x+3)+1/(x+6)

1/(x+2)-1/(x+3)=1/(x+6)-1/(x+7)

x^2+5x+6=x^2+13x+42

x=-4.5

Answer 2

两边同时减去2有
1/x+2 + 1/x+7 =1/x+3 + 1/x+6
1/x+2-1/x+3=1/x+6-1/x+7
1/(x+2)(x+3)=1/(x+6)(x+7)
x^2+5x+6=x^2+13x+42
所以x=-4.5

Answer 3

化简等式得：
1-1/(X+6)+1-1/(x+3)=1-1/(x+2)+1-1/(x+7)，整理得
1/(x+6)-1/(x+7)=1/(x+2)-1/(x+3)；
1/[(x+6) (x+7)]= 1/[(x+2) (x+3)];
故(x+6) (x+7)= (x+2) (x+3) ≠0；
所以x=-4.5