要计算过程：关于x的分式方程6/x-1=x+3/x(x-3)-k/x有解求k的取值范围?下面还有一题已知x y是方程组{x+2y=4 x-y=-5 的解求代数式x/x^2-2xy+y^2*x^2-y^2/x+y-2的值
2019-05-07
要计算过程：关于x的分式方程6/x-1=x+3/x(x-3)-k/x有解求k的取值范围?下面还有一题
已知x y是方程组{x+2y=4 x-y=-5 的解求代数式x/x^2-2xy+y^2*x^2-y^2/x+y-2的值
优质解答
6/x-1=x+3/x(x-3)-k/x
6x(x-3)=(x+3)(x-1）-k(x-1)(x-3)
6x^2-18x=x^+2x-3-kx^2+4kx-3k
-(k+5)x^+(20+4k)x-3k-3=0
(20+4k)^2-4(-(k+5))(-3k-3)>=0
400+160k+16k^2-12k^2-72k-60>=0
4k^2+88k+340>=0
k^2+22k+85>=0
（k+17)(k+5)>=0
k=-5
x+2y=4 x-y=-5
x=-2 y=3
x/x^2-2xy+y^2*x^2-y^2/x+y-2
=x/(x-y)^2*(x+y)(x-y)/x+y-2
=-2/(-5)*1/(1-2)
=-2/5
6/x-1=x+3/x(x-3)-k/x
6x(x-3)=(x+3)(x-1）-k(x-1)(x-3)
6x^2-18x=x^+2x-3-kx^2+4kx-3k
-(k+5)x^+(20+4k)x-3k-3=0
(20+4k)^2-4(-(k+5))(-3k-3)>=0
400+160k+16k^2-12k^2-72k-60>=0
4k^2+88k+340>=0
k^2+22k+85>=0
（k+17)(k+5)>=0
k=-5
x+2y=4 x-y=-5
x=-2 y=3
x/x^2-2xy+y^2*x^2-y^2/x+y-2
=x/(x-y)^2*(x+y)(x-y)/x+y-2
=-2/(-5)*1/(1-2)
=-2/5