若x\3y=y\(2x-5y)=(6x-15y)\x,求(4x²-5xy+6y)\（x²-2xy+3y²）括号的意思就是整体作分子或分母

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若x\3y=y\(2x-5y)=(6x-15y)\x,求(4x²-5xy+6y)\（x²-2xy+3y²）括号的意思就是整体作分子或分母若x\3y=y\(2x-5y)=(

若x\3y=y\(2x-5y)=(6x-15y)\x,求(4x²-5xy+6y)\（x²-2xy+3y²）括号的意思就是整体作分子或分母
若x\3y=y\(2x-5y)=(6x-15y)\x,求(4x²-5xy+6y)\（x²-2xy+3y²）
括号的意思就是整体作分子或分母

若x\3y=y\(2x-5y)=(6x-15y)\x,求(4x²-5xy+6y)\（x²-2xy+3y²）括号的意思就是整体作分子或分母
x/(3y)=y/(2x-5y)=(6x-15y)/x
x/(3y)=y/(2x-5y)--->2x^2-5xy-3y^2=0--->x=-y/2 or 3y--->x/y=-1/2;or 3
x/(3y)=(6x-15y)/x--->x^2-18xy+45y^2=0--->x=3y or 15y--->x/y=3 or 15
y/(2x-5y)=(6x-15y)/x--->12x^2-61xy+75y^2=0
--->x=3y;or 25y/12.
因为三个等式同时成立,有且只有x/y=3才成立--->x=3y.代入所求的分式:
(4x^2-5xy+6y^2)/(x^2-2xy+3y^2)
=(36y^2-15y^2+6y^2)/(9y^2-6y^2+3y^2)
=27/6
=9/2.

题目中分子错了请检查下

x\3y=y\(2x-5y)----1
x\3y=(6x-15y)\x -----2
两式联例得
2x^2-5xy-3y^2=0-----1
x^2-18xy+45y^2=0------2
消掉x^2得 y=0或 x=3y（y不得0）带入所求式子
得4 或（21y+6）\6y (y不得0）

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