已知M=2xy/x^2-y^2,N=x^2+y^2/x^2-y^2,用“+”或“—”连接M,N,有三种不同形式：M+N.M-N,N_数学解答

已知M=2xy/x^2-y^2,N=x^2+y^2/x^2-y^2,
用“+”或“—”连接M,N,有三种不同形式：M+N.M-N,N-M,请你任选其中一种进行计算,并化简求值,其中x:y=5：2

人气：350 ℃　时间：2020-02-05 07:29:56

解答

x:y=5:2
所以y=2x/5
M+N
=2xy/(x^2-y^2)+(x^2+y^2)/(x^2-y^2)
=(x^2+2xy+y^2)/(x^2-y^2)
=(x+y)^2/(x+y)(x-y)
=(x+y)/(x-y)
=(x+2x/5)/(x-2x/5)
=(7x/5)/(3x/5)
=7/3其他两个也算一下另两个重新问其他两个也算一下，我个你加分N-M=(x^2+y^2)/(x^2-y^2)-2xy/(x^2-y^2)=(x^2-2xy+y^2)/(x^2-y^2)=(x-y)^2/(x+y)(x-y)=(x-y)/(x+y)=(x-2x/5)/(x+2x/5)=(3x/5)/(7x/5)=3/7M-N=-(N-M)=-3/7