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(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)2x/x²-64y²-1/x-8y
题目详情
(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)2x/x²-64y²-1/x-8y
(3)2a/5a²b+3b/10ab² (4)2m/5n²p-3n/4mp² (5)3y/2x+2y+2xy/x²+xy (6)2x/x²-64y²-1/x-8y
▼优质解答
答案和解析
(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)
=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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