X/3 + X-1/6 = X+5/X(X-1) 分式方程

X/3 + X-1/6 = X+5/X(X-1) 分式方程
X/3 + X-1/6 = X+5/X(X-1) 分式方程

X/3 + X-1/6 = X+5/X(X-1) 分式方程
X=4
原式=(X-1)/(X-2)-(X-2)/(X-3)=(X-4)/(X-5)-(X-5)/(X-6)
左边通分=[X^2-4X+3-X^2+4X-4]/[(X-2)(X-3)] = -1/[(X-2)(X-3)]
右边通分=-1/[(X-5)(X-6)]
等式两边相等,同时去掉-1,原式可以化简为：X^2-11X+30=X^2-5X+6 即：
6X=24 X=4 满足题设分母不等于零的要求.