求过程。 （1）(x/2y)²乘y/2x-x/y²÷2y²/x （2）x+1/x乘（2x/x+1）²-（1/x-1-1/x+1）
（3）2a/5a²b+3b/10ab²(4）2m/5n²p-3n/4mp²（5）3y/2x+2y+2xy/x²+xy（6...
（3）2a/5a²b+3b/10ab² (4）2m/5n²p-3n/4mp² （5）3y/2x+2y+2xy/x²+xy （6）2x/x²-64y²-1/x-8y
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2013-12-24 · 知道合伙人教育行家
wangcai3882
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解：
（1）(x/2y)²乘y/2x-x/y²÷2y²/x
=x²/4y²*y/2x-x/y²*x/2y²
=x/8y-x²/2y⁴
=xy³/8y⁴-4x²/8y⁴
=(xy³-4x²)/8y⁴
（2）x+1/x乘（2x/x+1）²-（1/x-1-1/x+1）
=1/x*4x²/(x+1)-（1/x-1-1/x+1）
=4x/(x+1)-1/(x-1)+1/(x+1）
=(4x+1)/(x+1)-1/(x-1)
=[(4x+1)(x-1)-(x+1)]/(x+1)(x-1)
=(4x²-3x-1-x-1)/(x+1)(x-1)
=(4x²-4x-2)/(x+1)(x-1)
=(4x²-4x-2)/(x²-1)
（3）
2a/5a²b+3b/10ab²
=2/5ab+3/10ab
=4/10ab+3/10ab
=7/10ab
（4）
2m/5n²p-3n/4mp²
=2m*4mp/20mn²p²-3n*5n²/20mn²p²
=(8m²p-15n³)/20mn²p²
（5）3y/2x+2y+2xy/x²+xy
=3y/2(x+y)+2xy/x(x+y)
=3xy/2x(x+y)+4xy/2x(x+y)
=7xy/2x(x+y)
（6）
2x/x²-64y²-1/x-8y
=2x/(x+8y)(x-8y)-(x+8y)/(x+8y)(x-8y)
=(2x-x-8y)/(x+8y)(x-8y)
=(x-8y)/(x²-64y²)
（1）(x/2y)²乘y/2x-x/y²÷2y²/x
=x²/4y²*y/2x-x/y²*x/2y²
=x/8y-x²/2y⁴
=xy³/8y⁴-4x²/8y⁴
=(xy³-4x²)/8y⁴
（2）x+1/x乘（2x/x+1）²-（1/x-1-1/x+1）
=1/x*4x²/(x+1)-（1/x-1-1/x+1）
=4x/(x+1)-1/(x-1)+1/(x+1）
=(4x+1)/(x+1)-1/(x-1)
=[(4x+1)(x-1)-(x+1)]/(x+1)(x-1)
=(4x²-3x-1-x-1)/(x+1)(x-1)
=(4x²-4x-2)/(x+1)(x-1)
=(4x²-4x-2)/(x²-1)
（3）
2a/5a²b+3b/10ab²
=2/5ab+3/10ab
=4/10ab+3/10ab
=7/10ab
（4）
2m/5n²p-3n/4mp²
=2m*4mp/20mn²p²-3n*5n²/20mn²p²
=(8m²p-15n³)/20mn²p²
（5）3y/2x+2y+2xy/x²+xy
=3y/2(x+y)+2xy/x(x+y)
=3xy/2x(x+y)+4xy/2x(x+y)
=7xy/2x(x+y)
（6）
2x/x²-64y²-1/x-8y
=2x/(x+8y)(x-8y)-(x+8y)/(x+8y)(x-8y)
=(2x-x-8y)/(x+8y)(x-8y)
=(x-8y)/(x²-64y²)
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