Question

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

Answer 1

x+1/x+2 + x+6/x+7 = x+2/x+3 + x+5/x+6
即x+1/x+2-x+5/x+6=x+2/x+3-x+6/x+7
即：-4/[(x+2)*(x+6)]=-4/[(x+3)*(x+7)]
即当X+3不等于0且x+7不等于0且x+2不等于0且x+6不等于0时，
(x+2)*(x+6)=(x+3)*(x+7)
即8x+12=10X+21
即x=-9/2

Answer 2

（x+1）/(x+2）+(x+6)/(x+7)=(x+2）/(x+3）+(x+5）/(x+6）
（x+1）/(x+2)-(x+2）/(x+3)=(x+5）/(x+6)-(x+6)/(x+7)
-1/(x+2)(x+3)=-1/(x+6)(x+7)
-(x+6)(x+7)=-(x+2)(x+3)
x^2+13x+42=x^2+5x+6
8x=-36
x=-4.5

Answer 3

(X+1/X+2)-(X+2/X+3)=(X+5/X+6)-(X+6/X+7)
(X方+4X+3-X方-4X-4)/(X方+5X+6)=(X方+12X+35-X方-12X-36)/(X方+13X+42)
X方+5X+6=X方+13X+42
-8X=36
X=-9/2