根式化简计算题

(1)[(√a+√b)^2-4√ab]÷(√b-√a)

(2)2√1/8-√1/2-(√18+√2-2√1/3)

(3)(√24-√0.5-2√2/3)-(√1/8-√6)

(4)2a√3ab^2-b/6√27a^3+2ab√3/43,其中ab＞0

(5)(√12x-√y/2√-2√x/3)-2(√y/8-√18y)

每道题都要详细的过程和答案，谢谢！

(1)[(√a+√b)^2-4√ab]÷(√b-√a)
=(a+b-2√ab)÷(√b-√a)
=(√b-√a)²÷(√b-√a)
=√b-√a

(2)2√1/8-√1/2-(√18+√2-2√1/3)
=√1/2-√1/2-(3√2+√2-2√3/3)
=0-(4√2-2√3/3)
=-4√2+2√3/3

(3)(√24-√0.5-2√2/3)-(√1/8-√6)
=2√6-√2/2-2√2/3-√2/4+√6
=3√6-17√2/12

从一般到特殊: 因为1+1/n2+1/(n+1)2=(n2(n+1)2+(n+1)2+n2)/(n+1)2n2. =n4+2n3+3n2+2n+1/( )=n2+n+1+n(n2+n+1)+n2(n2+n+1)/ ( )=(n2+n+1)2/(n+1)2n2. 开根即得1+1/(n2+n). 所以原式=1+1/2,+1+1/6,+1+1/12,+....+1+1/2003*2004,=2003,+1-1/2,+1/2-1/3,+1/3-1/4,.......

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