分式的乘除

(1)（a²-a）÷a/a-1
=a(a-1)*(a-1)/a
=(a-1)^2
=a^2-2a+1
(2)-3a³b²/4cd³×3a²c²/21bd³÷-a^7/10d^6
=(-3a^3b^2)*(3a^2b^2)*(10d^6)/[(4cd^3)*(21bd^3)*(-a^7)]
=-90a^5b^4d^6/(-84a^7bcd^6)
=15b^3/(14a^2c)
（3）（x²-y²/xy）²÷（x+y）×（x/x-y)³
=（x+y)^2(x-y)^2(x-y)^3/[x^2y^2(x+y)]
=(x+y)(x-y)^5/(x^2y^2)
（4）若1/x-1/y=3
(y-x)/xy=3
y-x=3xy
x-y=-3xy
(2x+3xy-2y)/(x-2xy-y)
=[2(x-y)+3xy]/[(x-y)-2xy]
=(-6xy+3xy)/(-3xy-2xy)
=-3xy/(-5xy)
=3/5
（5）甲队在n天内挖水渠a米,乙队在m天内挖水渠b米,如果两队同时挖水渠,要挖x米,余姚多少天完成（用代数式表示）
甲一天挖a/m,乙b/n
所以需要x/(a/m+b/n)
=xmn/(an+bm)天
（6）已知a²+3a+1=0求下列各值
①a+1/a
把a=0代入
1=0,不成立
所以a不等于0
所以两边可以除以a
a+3+1/a=0
a+1/a=-3
②a²+1/a²
(a+1/a)^2=9
a^2+2a*1/a+1/a^2=9
a^2+2+1/a^2=9
a^2+1/a^2=7
③a³+1/a³
=(a+1/a)(a^2-1+1/a^2)
=-3*(7-1)
=-18
④a^4+1/a^4
(a^2+1/a^2)^2=49
a^4+2+1/a^4=49
a^4+1/a^4=47