2x/3y²×5y/6x÷y/x=______; a+2/a²-2a×a²-4a+4/a+2=______________;x-2/x²÷x+1/x²

题目

2x/3y²×5y/6x÷y/x=______; a+2/a²-2a×a²-4a+4/a+2=______________;x-2/x²÷x+1/x²+2x+1=__________;
x/x+y + y/x-y - 2xy/x²-y²=__________.

答案

2x/3y²×5y/6x÷y/x
=(2x*5y*x)/(3y²*6x*y)
=5x/(9y²)
a+2/a²-2a×a²-4a+4/a+2
=(a+2)(a-2)²/[a(a-2)(a+2)]
=(a-2)/a
=1-2/a
x-2/x²÷x+1/x²+2x+1
=(x-2)(x+1)²/[x²(x+1)]
=(x-2)(x+1)/x²
=(x²-x-2)/x²
x/x+y + y/x-y - 2xy/x²-y²
=[x(x-y)+y(x+y)-2xy]/(x²-y²)
=(x-y)²/(x-y)(x+y)
=(x-y)/(x+y)