A、B两地相距s千米,汽车以每小时x千米的速度从甲地到乙地去,走了y小时后,汽车速度每小时增加2千米,汽车从家地道一地共走了多少小时?

1.
设汽车速度为(x+2)千米/小时,走了t小时
x*y+(x+2)*t=s
t=(s-xy)/(x+2)
y+t=y+(s-xy)/(x+2)=(xy+2y+s-xy)/(x+2)=(s+2y)/(x+2)
汽车从甲地到乙地共走了(s+2y)/(x+2)小时
2.
[1/(a^2-a+1)-(1-a)/(a^3-1)]*[(a^6-1)-(a^4+a^2+1)]/(a^4-a^2-2)
=[1/(a^2-a+1)+(a-1)/(a-1)(a^2+a+1)]*[(a^2-1)(a^4+a^2+1)-(a^4+a^2+1)]/(a^2-2)(a^2+1)
=[1/(a^2-a+1)+1/(a^2-a+1)]*[(a^4+a^2+1)(a^2-2)]/(a^2-2)(a^2+1)
=[(a^2+a+1+a^2-a+1)/(a^2-a+1)(a^2-a+1)]*(a^4+a^2+1)/(a^2+1)
=2(a^2+1)/[(a^2+1)^2-a^2]*(a^4+a^2+1)/(a^2+1)
=2/(a^4+2a^2+1-a^2)*(a^4+a^2+1)
=2
3.
1/x+1/y=1①
1/y+1/z=2②
1/x+1/z=5③
①+②+③得
1/x+1/y+1/z=4
得,1/x=2,1/y=-1,1/z=3
x=1/2,y=-1,z=1/3
x^2y^2z^2
=(1/2)^2*(-1)^2*(1/3)^2
=1/36