若2x^2-6xy+9y^2-4x+4=0,则y/x-x/y=

[(x-y)/(x+3y)]/[(x^2-y^2)/(x^2+6xy+9y^2)]-xy/(x+y)
=(x-y)/(x+3y) * (x+3y)^2/(x-y)(x+y)-xy/(x+y)
=(x+3y)/(x+y)-xy/(x+y)
=(x-xy+3y)/(x+y)
=1-y(x-2)/(x+y)

1、（x-1)^2-(y+z)^2=(x-y-z-1)(x+y+z-1)
2、(x-3y)^2-10(x-3y)+25=(x-3y-5)^2
3、(a-b)(a+b)-ab(a-b)-(a-b)=(a-b)(-ab+a+b-1)=(b-a)(a-1)(b-1)
4、（x^2+2)(x^2-2)+3x(x^2+2)=(x^2+2)(x^2+3x-2)
5、(a^2-b^2-c^2-2bc)(a^2-b^2-c^2+2bc)=[a^2-(b+c)^2][a^2-(b-c)^2]
=(a+b+c)(a-b-c)(a-b+c)(a+b-c)
6、(x-y)^2-4(x-y)+4=(x-y-2)^2
7、(x^2+2y^2)^2-4x^2y^2=(x^2+2xy+2y^2)(x^2-2xy+2y^2)
8、-xy

x ² -6xy+9y ² --3/2x+9/2y+m/2
=( x -3y)²-3/2(x-3y)+m/2
因上式为一个完全平方式,故即为〔( x -3y)-3/4〕²
（3/4)² =m/2 求得m=9/8

题出错了吧应该是2x+6y/（x-3y）, x/（x^2-9y^2）, 1/（x^2-6xy+9y^2）吧?如果是这个通分结果：分母（x+3y）*（x-3y）^2.分子分别为：2（x+3y）^2*（x-3y）,x*（x-3y）,x+3y.

因为2x^2-6xy+9y^2-4x+4=0,所以x^2-6xy+9y^2+x^2-4x+4=0 (x-3y)^2+(x-2)^2=0 x-3y=0,x-2=0 所以x=2,y=2/3 故x+3y=2+3×（2/3）=2+2=4

因为2x^2-6xy+9y^2-4x+4=0
所以x^2-4x+4+x^2-6xy+9y^2=0
(x-2)^2+(x-3y)^2=0
所以x-2=0,x-3y=0
所以y=2/3
√y=√6/3

(2x+3y)(2x-3y)(4x^2+6xy+9y^2)(4x^2-6xy+9y^2)
=(2x+3y)(2x-3y)(2x+3y)^2(2x-3y)^2
=(2x+3y)^3(2x-3y)^3
不知道你这道题有什么要求,再算一步也可以,就是
＝（4x^2-9y^2)＾3

x/y=2/3
所以y=3x/2
原式=[5y²-(x-2y)(x+2y)]/(x-2y)÷(x-3y)²/(x-2y)
=(9y²-x²)/(x-2y)*(x-2y)/(x-3y)²
=-(x+3y)(x-3y)/(x-2y)*(x-2y)/(x-3y)²
=-(x+3y)/(x-3y)
=-(x+3x/2)/(x-3x/2)
=5

x^2-6xy+9y^2-10x+30y+25
=(x-3y)^2-10(x-3y)+25
=(x-3y-5)^2

1.x^2-3xy/x^2-6xy+9y^2=（x-3y）²-3y/x
将x=-1,y=2/3代入得：（-1-3×2/3）²-3×2/3÷（-1）=11
2.a^2-2ab+b^2/b-a=（a-b）²÷（b-a）=b-a
3.m^2-2m+1/m-1+4-m^2/m+2=（m-1）²÷（m-1）+（2+m）（2-m）÷（m+2）=m-1+2-m=1

(2x-3y)(4x²+6xy+9y²)
=2x(4x²+6xy+9y²)-3y(4x²+6xy+9y²)
=8x³+12x²y+18xy²-12x²y-18xy²-27y³
=8x³-27y³
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