若1/m-1/n=3,求2m-3mn-2n/m-2mn-m的值以知xyz不等于0且x+3y+7z=0,3x-4y-18z=0求3x^2+5y^2+6z^2/x^2+2y^2+8z^的值若1/x-1/y=3则分式2x+3xy-2y/x-2xy-y的值我要的是过程

Question

若1/m-1/n=3,求2m-3mn-2n/m-2mn-m的值
以知xyz不等于0 且x+3y+7z=0,3x-4y-18z=0 求3x^2+5y^2+6z^2/x^2+2y^2+8z^的值
若1/x-1/y=3 则分式 2x+3xy-2y/x-2xy-y的值
我要的是过程

Answer 1

(1)是(2m-3mn-2n)/(m-2mn-n)吧?
1/m-1/n=3
(n-m)/mn=3
n-m=3mn
(2m-3mn-2n)/(m-2mn-n)
=[2(m-n)-3mn]/[(m-n)-2mn]
=(-6mn-3mn)/(-3mn-2mn)
=9mn/5mn
=9/5
(2)
x+3y+7z=0
3x-4y-18z=0
解方程组：
y=-3x/2
z=x/2
(3x^2+5y^2+6z^2)/(x^2+2y^2+8z^2)
=[3x^2+5*(-3x/2)^2+6(x/2)^2]/[x^2+2(-3x/2)^2+8(x/2)^2]
=(3x^2+45x^2/4+3x^2/2)/(x^2+9x^2/2+2x^2)
=(3+45/4+3/2)/(1+9/2+2)
=(12+45+6)/(4+18+8)
=63/30
=21/10
(3)
1/x-1/y=3
(y-x)/xy=3
y-x=3xy
(2x+3xy-2y)/(x-2xy-y)
=[3xy-2(y-x)]/[(x-y)-2xy]
=(3xy-6xy)/(-3xy-2xy)
=3xy/5xy
=3/5