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郭敦顒回答:
(2)1-8/(a²-4)•{[(a²+4)/4a-1]/(1/2-1/a)}
=1-8/(a²-4)•{[(a²+4-4a)/4a]/[(a-2)/2 a]}
=1-8/[(a+2)(a-2)]•{[(a-2)²]/[2(a-2)]}
=1-8/[2(a+2)]
=1-4/(a+2)
(3){2/3x-[2/(x+y)][(x+y)/3x-x-y]}/[(x-y)/x]
= x {2/3x-[2/(x+y)][(x+y)/3x-(x+y)]}/(x-y)
=x{[2(x+y)/9x²]-[2(x+y)/3x] -(2/3x)+2 }/(x-y)
=[2(x+y)/9x(x-y)]-[2(x+y)/3(x-y)] -2/[3(x-y)]+2/[x(x-y)]
四2,设甲单独做需x天,乙单独做需y天,丙单独做需z天,则
x=a(1/y+1/z),a=x/(1/y+1/z)=x/[(y+z)/yz]= xyz/(y+z),
y=b(1/x+1/z),b=y/(1/x+1/z)= xyz/(x+z),
z=c(1/y+1/x),c=z/(1/y+1/x)= xyz/(y+ x)
1/(a+1)+1/(b+1)+1/(c+1)
=1/[ x/(1/y+1/z)+1]+ 1/[ y/(1/x+1/z)+1]+ 1/[ z/(1/y+1/x)+1]
=1/[ xyz/(y+z)+1]+ 1/[ xyz/(x+z)+1]+ 1/[ xyz/(y+x)+1]
=[(y+z)/( xyz+y+z)]+ [(x+z)/( xyz+x+z)]+ [(y+x)/( xyz+y+x)]
(2)1-8/(a²-4)•{[(a²+4)/4a-1]/(1/2-1/a)}
=1-8/(a²-4)•{[(a²+4-4a)/4a]/[(a-2)/2 a]}
=1-8/[(a+2)(a-2)]•{[(a-2)²]/[2(a-2)]}
=1-8/[2(a+2)]
=1-4/(a+2)
(3){2/3x-[2/(x+y)][(x+y)/3x-x-y]}/[(x-y)/x]
= x {2/3x-[2/(x+y)][(x+y)/3x-(x+y)]}/(x-y)
=x{[2(x+y)/9x²]-[2(x+y)/3x] -(2/3x)+2 }/(x-y)
=[2(x+y)/9x(x-y)]-[2(x+y)/3(x-y)] -2/[3(x-y)]+2/[x(x-y)]
四2,设甲单独做需x天,乙单独做需y天,丙单独做需z天,则
x=a(1/y+1/z),a=x/(1/y+1/z)=x/[(y+z)/yz]= xyz/(y+z),
y=b(1/x+1/z),b=y/(1/x+1/z)= xyz/(x+z),
z=c(1/y+1/x),c=z/(1/y+1/x)= xyz/(y+ x)
1/(a+1)+1/(b+1)+1/(c+1)
=1/[ x/(1/y+1/z)+1]+ 1/[ y/(1/x+1/z)+1]+ 1/[ z/(1/y+1/x)+1]
=1/[ xyz/(y+z)+1]+ 1/[ xyz/(x+z)+1]+ 1/[ xyz/(y+x)+1]
=[(y+z)/( xyz+y+z)]+ [(x+z)/( xyz+x+z)]+ [(y+x)/( xyz+y+x)]
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