先化简,再求值,﹙1/x-y-1/x+y﹚÷2y/x²+2xy+y²,其中x=√3+√2,y=√3-√2

题目

先化简,再求值,﹙1/x-y-1/x+y﹚÷2y/x²+2xy+y²,其中x=√3+√2,y=√3-√2

答案

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