1.x^2-1/x^2+2x+1÷2x^2-2/ax^2+8x+4÷(x-1)^22.(x^2-y^2/xy)^2÷(x+y)·(x/x-y)^33.已知分式x^3-2x^2y/x^2y-2xy^2,其中x=3,y=14.已知x/y=1/2,求x^2+2xy+y^2/x^2-xy-2y^2的值5.已知x^2+x-1=0,求①(1/x^2)+x^2②x^4+(1/x^4).6.如果1/x-1/y=3,求3x-2x

Question

1.x^2-1/x^2+2x+1÷2x^2-2/ax^2+8x+4÷(x-1)^2
2.(x^2-y^2/xy)^2÷(x+y)·(x/x-y)^3
3.已知分式x^3-2x^2y/x^2y-2xy^2,其中x=3,y=1
4.已知x/y=1/2,求x^2+2xy+y^2/x^2-xy-2y^2的值
5.已知x^2+x-1=0,求①(1/x^2)+x^2 ②x^4+(1/x^4)
.
6.如果1/x-1/y=3,求3x-2xy-3y/x+xy-y的值

Answer 1

1、
(x^2-1)/(x^2+2x+1)=(x-1)(x+1)/(x+1)^2=(x-1)/(x+1)
(2x^2-2))/(4x^2+8x+4)=(x-1)/[2(x+1)]
前2个的结果：2
最后化简为：2/(x-1)^2
2、
=[(x-y)(x+y)/xy]^2*[1/(x+y)]*(x^3/(x-y)^3]
=(x-y)^2*x^3(x+y)/[x^2y^2(x-y)^3
=x(x+y)/[y^2(x-y)]
这些分式计算在网上很不好表达,凑合着看吧
3、
x^2(x-2y)/[xy(x-2y)]
=x/y=3/1=3
4、
分子分母同时÷xy
原式=[(x/y)+2+(y/x)]/[(x/y)-1-2(y/x)]
=(1/2+2+2)/(1/2-1-4)
=4.5/(-4.5)=-1
5、
x^2+x+1=0
x+1+1/x=0
x+1/x=-1
(x+1/x)^2=1
x^2+1/x^2+2=1
x^2+1/x^2=-1.①
②
(x^2+1/x^2)^2=1
x^4+1/x^4+2=1
x^2+1/x^4=-1
6、
分子分母同时÷xy
原式=(3/y-2-3/x)/(1/y+1-1/x)
=(-2-9)/(1-3)=11/2