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化简
(1)(-2a) ³ b ⁴÷12a ³b²
(2)x - 1/x÷(x - 1/x)
(3)x-y/x+2y ÷ x²-y²/x²+4xy+4y² -2,x=2-√2 ,y=2√2-1
(4)2-x/x-1÷(x+1 - 3/x-1)
(5)x-2/x+2 - x+2/x-2,x=√2
(6)1/a+1 - a+3/a² -1 乘 a² -2a+1/a² +4a+3 ,a满足a² +2a-1=0
(7)1 - x-y/x+2y ÷ x²-y²/x²+4xy+4y² ,x=√2,y=1
(1)(-2a) ³ b ⁴÷12a ³b²
=-8a³b ⁴÷12a ³b²
=-2/3b²
(2)x - 1/x÷(x - 1/x)
=x-1/(x²-1)
=(x³-x-1)/(x²-1)
(3)x-y/x+2y ÷ x²-y²/x²+4xy+4y² -2,x=2-√2 ,y=2√2-1
=(x-y)/(x+2y)×(x+2y)²/(x-y)(x+y)
=(x+2y)/(x+y)
=(2-√2+4√2-2)/(2-√2+2√2-1)
=3√2/(√2+1)
=3√2(√2-1)
=6-3√2
(4)2-x/x-1÷(x+1 - 3/x-1)
=(2-x)/(x-1) ÷(x²-4)/(x-1)
=(2-x)/(x-2)(x+2)
=-1/(x+2)
(5)x-2/x+2 - x+2/x-2,x=√2
=(x²-4x+4-x²-4x-4)/(x+2)(x-2)
=(-8x)/(x²-4)
=-8√2/(2-4)
=4√2
(6)1/a+1 - a+3/a² -1 乘 a² -2a+1/a² +4a+3 ,a满足a² +2a-1=0
=1/a+1 -(a+3)/(a+1)(a-1) ·(a-1)²/(a+1)(a+3)
=1/(a+1) -(a-1)/(a+1)²
=(a+1-a+1)/(a+1)²
=2/(a²+2a+1)
=2/(1+1)
=1
(7)1 - x-y/x+2y ÷ x²-y²/x²+4xy+4y² ,x=√2,y=1
=1-(x-y)/(x+2y)×(x+2y)²/(x+y)(x-y)
=1- (x+2y)/(x+y)
=(x+y-x-2y)/(x+y)
=-y/(x+y)
=-1/(√2+1)
=-(√2-1)
=-√2+1