①已知1/x-1/y=3,求5x+xy-5y/x-xy-y的值.②已知m>n>0,m^2+n^2=4mn,求m^2-n^2/mn的值.(请把这两道分式题的推算过程写详细些,)

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/16 19:29:42
①已知1/x-1/y=3,求5x+xy-5y/x-xy-y的值.②已知m>n>0,m^2+n^2=4mn,求m^2-n^2/mn的值.(请把这两道分式题的推算过程写详细些,)①已知1/x-1/y=3,

①已知1/x-1/y=3,求5x+xy-5y/x-xy-y的值.②已知m>n>0,m^2+n^2=4mn,求m^2-n^2/mn的值.(请把这两道分式题的推算过程写详细些,)
①已知1/x-1/y=3,求5x+xy-5y/x-xy-y的值.
②已知m>n>0,m^2+n^2=4mn,求m^2-n^2/mn的值.(请把这两道分式题的推算过程写详细些,)

①已知1/x-1/y=3,求5x+xy-5y/x-xy-y的值.②已知m>n>0,m^2+n^2=4mn,求m^2-n^2/mn的值.(请把这两道分式题的推算过程写详细些,)
∵1/x-1/y=3
∴y-x=3xy
(5x+xy-5y)/(x-xy-y)=(5x-5y+xy)/(x-y-xy)=(-15xy+xy)/(-3xy-xy)=3.5
∵m²+n²=4mn
∴m²+n²-2mn=2mn
∴(m-n)²=2mn
又∵m>n>0
∴m-n=√(2mn)
∵m²+n²=4mn
∴m²+n²+2mn=6mn
∴(m+n)²=6mn
又∵m>n>0
∴m+n=√(6mn)
∴(m²-n²)/mn=(m+n)(m-n)/mn=2√3
累死我了,请求加分!

(1)5x+xy-5y/x-xy-y
=(5/y-5/x+1)/(1/y-1/x-1)
=(1-15)/(-3-1)
=7/2;
(2)m²+n²-2mn=2mn;
(m-n)²=2mn;
(m+n)²=6mn;
(m²-n²)/mn=√(6mn)(2mn)/mn=2√3;