{2x y=8 3x-y=7

已知x/y=7/2,(2x²+3xy+2y²)/(x²+2xy+y²)=(2x/y+3+2y/x)/(x/y+2+y/x)=(2×7/2+3+2×2/7）/（7

(x^2-3XY+2Y^2)/(X^2-2XY+Y^2)=(x-2y)(x-y)/(x-y)^2=(x-2y)/(x-y)=(x-y-y)/(x-y)=1-y/(x-y)=1-1/(x/y-1)=1-

x-xy=8(1)xy-y=-9(2)则有(1)-(2):X-XY-XY+Y=X+Y-2XY=8-(-9)=17

第一题设x+y=axy=b则x^2+y^2=a^2-2b原方程变为a^2-2b+b=13①b+a=7②这就变成了简单的二元二次方程由②得b=7-a带入①得a^2+a-20=0（a-4)(a+5)=0得

(-3x^y+2xy)-(4x^+xy)=-3x^y+2xy-4x^-xy=-3x^y+xy-4x^所以填上-3x^y+xy-4x^

原式=6x+4xy+2xy+3x+2y-4xy+7y=9x+9y+2xy=9(x+y)+2xy=9×4+2×2=36+4=40

将1/x-1/y=5通分,得y-x/xy=5,两边同时乘以xy,得y-x=5xy,带入-x+xy+y/2x+7xy-2y,得5xy+xy/-2*5xy+7xy,合并同类项,得6xy/-3xy=-2即,

x^2y+xy^2=xy（x+y）=7x6=42再问：��(x+1)^2=13��x^2+2x+3=再答：x^2+2x+3=（x+1）^2+2=13+2=15

（4xy+12y)+[7x-(3xy+4y-x)]=4xy+12y+7x-3xy-4y+x=xy+8x+8y=xy+8(x+y)=(-2)+8*3=-2+24=22

最简单的方法就是用特殊值,令x=-2,y=1然后代入所求表达式,求出其值.为-8；另外此内题的另一个解法是变化所求表达式,使它变成关于xy^2的表达式.

解题方法：分子、分母同时除一个xy(y+xy-x)/(2x+7xy-2y)=[(y+xy-x)/xy]/[(2x+7xy-2y)/xy]=(1/x+1-1/y)/(2/y+7-2/x)=[(1/x-1

(y+xy-x)/(2x+7xy-2y)(分子、分母同除一个xy)=(1/x+1-1/y)/(2/y+7-2/x)=6/(-10+7)=-2

设X=kY.kY^2/(3k+2)Y=1/8kY^2/((2k+3)Y=1/7由上式得：3k+2=8kY,2k+3=7kY所以2/（8Y-3）=3/（7Y-2）所以Y=1/2,X=1

∵x-y=4xy，∴2x+3xy-2yx-2xy-y=2(x-y)+3xyx-y-2xy=8xy+3xy4xy-2xy=112．故答案为：112．

(5xy+4x+7y)+(6x-3xy)-(4xy-3y)=5xy+4x+7y+6x-3xy-4xy+3y=(5xy-3xy-4xy)+(4x+6x)+(7y+3y)=-2xy+10x+10y=-2x

X²+2xy+y²/xy乘x²-2xy+y²/xy+y²=(x+y)²/xy×(x-y)²/y(x+y)=(x+y)(x-y)&#

（-x+xy+y）/(2x+7xy-2y)=(1/x-1/y+1)/(7-2(1/x-1/y))=(5+1)/(7-10)=6/(-3)=-2

因为x-y=-2xy所以将x-y都换成-2xy了

x²-7xy+12y²=0(x-3y)(x-4y)=0x1=3yx2=4yx=3y时原式＝9y²-3y²+y²/6y²=7/6x=4y时原式

[(x-y)^2+2xy-y^2]/[x^2+7xy+y^2]=[x²-2xy+y²+2xy-y²]/[x^2+7xy+y^2]=x²/[x^2+7xy+y^2