已知2x=3y,求xy/(x2+y2)-y2/(x2-y2)的值
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已知2x=3y,求xy/(x2+y2)-y2/(x2-y2)的值
题中的x2表示x的平方
题中的x2表示x的平方
已知2x=3y,求xy/(x^2+y^2)-y^2/(x^2-y^2)的值
2x=3y-->
x=(3/2)y
x^2=(9/4)y^2
xy/(x^2+y^2)-y^2/(x^2-y^2)=
=(3/2)y*y/[(9/4)y^2+y^2]-y^2/[(9/4)y^2-y^2]=
=(3/2)y^2/[(13/4)y^2]-y^2/[(5/4)y^2]=
=(3/2)*(4/13)-(4/5)=
=6/13-4/5=
=30/65-52/65=
=-22/65
2x=3y-->
x=(3/2)y
x^2=(9/4)y^2
xy/(x^2+y^2)-y^2/(x^2-y^2)=
=(3/2)y*y/[(9/4)y^2+y^2]-y^2/[(9/4)y^2-y^2]=
=(3/2)y^2/[(13/4)y^2]-y^2/[(5/4)y^2]=
=(3/2)*(4/13)-(4/5)=
=6/13-4/5=
=30/65-52/65=
=-22/65
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