原式=[(x-1)(x+2)]分之[x(x+2) -3 - (x-1)(x+2)]
=[(x-1)(x+2)]分之(x²+2x -3 - x²-x+2)
=[(x-1)(x+2)]分之(x -1)
=(x+2)分之1
其中:x≠1且x≠-2
x/(x-1)-3/[(x-1)(x+2)]-1
通分,将第一个式子分子分母同时乘以(x+2)。然后花间就行了,最后一个1变成。至于取值范围,分母不为0就行了,x不能取1且不能取-2
x/(x-1)-3/[(x-1)(x+2)]-1
=[x(x+2)-3]/[(x-1)(x+2)]-1
=(x²+2x-3)/[(x-1)(x+2)]-1
=(x+3)/(x+2)-1
=1/(x+2)
根据表达式分母不能为0,得x≠1且x≠-2
1/(x+2) x不等于-2