化简{x²-2x分之x+2-x²-4x+4x分之x-1}除以X分之(x-1)(X-4)乘以（2-x）²

题目

化简{x²-2x分之x+2-x²-4x+4x分之x-1}除以X分之(x-1)(X-4)乘以（2-x）²

答案

原式=[(x+2)/x(x-2)-(x-1)/(x-2)²]*x/(x-1)(x-4)*(x-2)²
=(x²-4-x²+x)/x(x-2)²*x/(x-1)(x-4)*(x-2)²
=1/(x-1)