先化简,再求值：（x-y分之一+x+y分之一）÷x的平方-y的平方分之x的平方y,其中x=根号3+1,y=根号3-1_数学解答

先化简,再求值：（x-y分之一+x+y分之一）÷x的平方-y的平方分之x的平方y,其中x=根号3+1,y=根号3-1

人气：438 ℃　时间：2019-08-23 06:34:53

解答

[1/(x-y)+1/(x+y)]÷(x^2y)/(x^2-y^2)
=[(x+y+x-y)/(x-y)(x+y)]÷(x^2y)/(x+y)(x-y)
=[2x/(x-y)(x+y)]÷(x^2y)/(x+y)(x-y)
=2x/(x^2y)
=2/(xy)
=2/[(√3+1)×(√3-1)]
=2/2
=1