先化简,再求值,﹙1/x-y-1/x+y﹚÷2y/x²+2xy+y²,其中x=√3+√2,y=√3-√2
问题描述：
先化简,再求值,﹙1/x-y-1/x+y﹚÷2y/x²+2xy+y²,其中x=√3+√2,y=√3-√2
答
原式=x²/[xy(x+y)]-y²/[xy(x+y)]
=(x²-y²)/[xy(x+y)]
=(x+y)/(x-y)/[xy(x+y)]
=(x-y)/(xy)
=[(√2+1)-(√2-1)]/[(√2+1)(√2-1)]
=(√2+1-√2+1)/(√2²-1²)
=2/(2-1)
=2
答
即x+y=2√3
x-y=2√2
原式=(x+y-x+y)/(x+y)(x-y)÷2y/(x+y)²
=2y/(x+y)(x-y)*(x+y)²/2y
=(x+y)/(x-y)
=2√3/2√2
=√6/2