x除以3=y除以4,求分式x^2+y^2分之x^2-xy

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x除以3=y除以4,求分式x^2+y^2分之x^2-xy

x除以3=y除以4,求分式x^2+y^2分之x^2-xy
x除以3=y除以4,求分式x^2+y^2分之x^2-xy

x除以3=y除以4,求分式x^2+y^2分之x^2-xy
x/3=y/4
所以x=3y/4
所以(x^2-xy)/(x^2+y^2)=(9y^2/16-3y^2/4)/(9y^2/16+y^2)=-3/25

x/3=y/4
x/y=3/4
(x²-xy)/(x²+y²)
上下同时除以y²
=[(x²/y²)-(x/y)]/[(x²/y²)+1]
=[(x/y)²-(x/y)]/[(x/y)²+1]
代入x/y=3/4
=[(3/4)²-(3/4)]/[(3/4)²+1]
=(9/16-3/4)/(9/16+1)
=(9-12)/(9+16)
=-3/25

令x/3=y/4=n,则x=3n.y=4n,
(x^2-xy)/(x^2+y^2)=(9n^2-3n*4n)/(9n^2+16n^2)
=-3/25;
若x=y=0,则原式的值不存在。

x/3=y/4所以y=(4x)/3
原式=x^2+y^2分之x^2-xy=[x^2-x*(4x)/3]/[x^2+(4x)^2/3^2]=(1-4/3)/(1+16/9)=-(1/3)/(25/9)=-(1/3)*(9/25)=-3/25

x/3=y/4=n,则x=3n.y=4n,
(x^2-xy)/(x^2+y^2)=(9n^2-3n*4n)/(9n^2+16n^2)
=-3/25;
若x=y=0

x:y =4:3
用极限做,2x^2-xy/x^2+y^=x-y/2x+2y,最后把x=4,y=3直接代入,得到1/12