6已知x+y=2,x-y=1,求分式x方2xy+y方分之x方-y方的值.

6已知x+y=2,x-y=1,求分式x方+2xy+y方分之x方-y方的值
x方+2xy+y方分之x方-y方
=(x+y)(x-y)/(x+y)²
=(x-y)/(x+y)
=1/2
7已知x分之1-y分之1=3,求分式x-2xy-y分之2x+3xy-2y的值.
1/x-1/y=3
∴(y-x)/xy=3
y-x=3xy
x-y=-3xy
x-2xy-y分之2x+3xy-2y
=[3xy+2(x-y)]/[-2xy+(x-y)]
=(3xy-6xy)/(-2xy-3xy)
=3/5
8先化简分式x方-2x+1分之6x-6,再讨论：当整数x取何值时,能使分式的值是整数?
x方-2x+1分之6x-6
=6(x-1)/(x-1)²
=6/(x-1)
∴x-1=-6、-3、-2、-1、1、2、3、6
∴x=-5、-2、-1、0、2、3、4、7
9已知ab分之a+b=6,bc分之b+c=8,ac分之a+c=10,其中a,b,c为任意实数.求分式abc分之ab+bc+ca的值
ab分之a+b=6,bc分之b+c=8,ac分之a+c=10
∴1/a+1/b=6
1/b+1/c=8
1/a+1/c=10
三式相加得
2/a+2/b+2/c=24
∴1/a+1/b+1/c=12
∴(ab+bc+ac)/abc=12