(1)a³+1=(a+1)(a²-a+1)
(2)b²+c²+2ab+2ac+2bc=(b+c)²+2a(b+c)=(b+c)(b+c+2a)
(3)3x²+5xy-2y²+x+9y-4=(3x-y)(x+2y)+x+9y-4
=(3x-y)(x+2y)-(3x-y)+4x+8y-4
=(3x-y)(x+2y-1)+4(x+2y-1)
=(3x-y+4)(x+2y-1)
(4)x+y/x-y=x²-y²/(x-y)²=2xy/x²+y²+x²-y²=2xy/2x²=y/x
(5)因为(x²+1/x²)=(x+1/x)²-2*x*1/x=(x+1/x)²-2
所以设a=x+1/x
2（a²-2）-3a-1=0
a=-1（舍）或5/2
所以x=5±√17/4
（6）由根号下-a分之1知-1/a≥0
所以a≤0
所以原式=√[-a*(-a)*(-1/a)]=√-a