已知x/y =2,求(x^2-xy+3y^2)/(x^2+xy+6y^2) 的值．

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已知x/y =2,求(x^2-xy+3y^2)/(x^2+xy+6y^2) 的值．
已知x/y =2,求(x^2-xy+3y^2)/(x^2+xy+6y^2) 的值．

已知x/y =2,求(x^2-xy+3y^2)/(x^2+xy+6y^2) 的值．
x/y =2,--->x=2y
(x^2-xy+3y^2)/(x^2+xy+6y^2)
=(4y^2-2y^2+3y^2)/(4y^2+2y^2+6y^2)
=5/12

x/y=2
x=2y
(x^2-xy+3y^2)/(x^2+xy+6y^2)
=(4y^2-2y^2+3y^2)/(4y^2+2y^2+6y^2)
=5y^2/12y^2
=5/12

原式=((x/y)^2-x/y+3)/((x/y)^2+x/y+6)
代入x/y=2
=(2^2-2+3)/(2^2+2+6)
=(4-2+3)/(4+2+6)
=5/12
其实只要将（x^2-xy+3y^2） /（x^2+xy+6y^2）分子分母同除以y^2 就解了

x/y=2
则y/x=1/2
(x^2-xy+3y^2)/(x^2+xy+6y^2)
=(x/y-1+3y/x)/(x/y+1+6y/x)
=(2-1+3/2)/(2+1+3)
=5/12

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