Question

先化简,再求值：(1/x-y - 1/x+y)÷2y/x的平方-2xy+y的平方,其中x=1

Answer 1

x=1+√2,y=1-√2x+y=2 x-y=2√2[（1/（x-y)+1/(x+y)]-【2y/（x的平方-2xy+y的平方）】 =[（x+y+x-y/（x-y)(x+y)]-【2y/（x-y）^2】=[2(1+√2)/2*2√2]-【2(1-√2)/（2√2）^2】=[(1+√2)/2√2]-【2(1-√2)/8】 =[(2+√2)/4]-【(1-√2)/4】 =(1+2√2)/4