(1-x²)(1-y²)-4xy

解题思路：用x2的取值范围、二次函数的的性质、均值不等式，换元法求函数的值域解题过程：

原式=(9x²+24xy+16y²-4x²+y²-5x²+6xy-y²)÷(-2y)=(30xy+16y²)÷(-2y)=-15x

3(x+y)+3(y-x)=1(1)3(x+y)+4(y-x)=-1(2)(2)-(1)得y-x=-2(3)代入（1）3（x+y)-6=1x+y=7/3=>x=7/3－y又由（3）得x=y+2y+2=

1,(x-y)³-(x-y)²(x+y)=(x-y)²(x-y-x-y)=-2y(x-y)²2,x(x²-xy)-(4x²-4xy)=x&#

1、4(x-y+1)+y(y-2x)=4x-4y+4+y²-2xy=y²-4y+4-2xy+4x=(y-2)²-2x(y-2)=(y-2x-2)(y-2)2、4x^4-1

原始=(4x²-4xy+y²+4x²-y²-4x²+4xy-4x)÷2x=(4x²-4x)÷2x=4x²÷2x-4x÷2x=2x-

（x+2)(x+3)=x²+5x+6(x-4)(x+1)=x²-3x-4(y+4)(y-2)=y²+2y-8(y-5)(y-3)=y²-8y+15x²

1)x(x-y)(x+y)-x(x+y)^2=x((x-y)(x+y)-(x+y)^2)=x(x^2-y^2-x^2-2xy-y^2)=x(-2xy-2y^2)=-2xy(x+y)2)（2a+b)(2

4（x-y+1)+y(y-2x)=4x-4y+4+y^2-2xy=(y^2-4y+4)-2x(2-y)=(y-2)^2+2x(y-2)=(y-2)(2x+y-2)

4(x-y+1)+y(y-2x)=4x-4y+4+y^2-2xy=(2-y)^2+2x(2-y)=(2-y)(2-y+2x)4x^4-13x²+9=4x^4-12x^2+9-x^2=(2x^

1)(2x+5y)(2x-5y)(-4x^2-25y^2)=-(4x^2-25y^2)(4x^2+25y^2)=-(16x^4-625y^4)=625y^4-16x^42)[（x+y)(x-y)-(x

（1)x^2/x)-y-x-y=x-y-x-y=-2y(2)(a/a-b)-(a/a+b)-(2b^2/a^2-b^2)=a(a+b-a+b)/(a^2-b^2)-(2b^2/a^2-b^2)=2b/

1/(x-y)-1/(x+y)-2y/(x^2+y^2)-4y^3/(x^4+y^4)-8y^7/(x^8+y^8)=【（x+y)-(x-y)】/(x-y)(x+y)-2y/(x^2+y^2)-4y^

3(x+y)-4(x-y)=4(x+y)/2+(x-y)/6=1令a=x+y,b=x-y3a-4b=4(1)a/2+b/6=1则3a+b=6(2)(2)-(1)5b=2b=2/5a=(6-b)/3=2

4x=9yx=9/4*y(1)(x+y)/y=[(9/4)y+y]/y=(9/4+1)y/y=9/4+1=13/4(2)(y-x)/2x=[y-(9/4)y]/[2*(9/4)y]=(1-9/4)y/

x²+xy/(x-4y)(x+y)=x(x+y)/(x-4y)(x+y)=x/(x-4y)=4/(4+4)=1/2

解9y=3x-(x-1)2x-9y+1=0①4(x+y)-(2x+4)=8y2x-4y-4=0②②-①得：5y-5=0∴y=1将y=1代入①得：2x-9+1=0∴x=4∴方程的解为：x=4,y=1

1,-3再问：过程。。。再答：★（x²－2x)+（y²－4y）=5★（x－1）²+（y－2）²=1+4－5★（x－l）²=0,（y－2）²=

完整设1/(x+y)=a,1/(x-y)=b原方程组可变为4a+6b=39b-a=1a=9b-136b-4+6b=3b=1/6,a=1/2x+y=2x-y=6所以原方程组的解为：x=4,y=-2

原式=x-x+x-x+……-x+(2-1+4-3+5-4+……+2008-2007-2009）y=0+(1×1004-2009)y=-1005y=1005/2