Question

整式的除法

1.(5m^3n^2)/(3m)
2.(6a^2b-5a^2c^2)/(-3a^2)
3.(16x^4+4x^2+x)/x
4.(3a^2b-2ab+2ab^2)/(ab)
5.(-4a^3+6a^2b^3+3a^3b^3)/(-4a^2)
6.(2/5mn^3-m^2n^2+1/6n^4)/(2/3n^2)
7.(1/10xy^2+1/4y^2-1/2y)/(1/5y)
8.[(x+1)(x+2)-2]/x
写过程

Answer 1

解1题
原式=(5÷3)×(m³÷m)×n²
=(5/3)×m^(3-1)×n²
=(5/3)m²n²

解2题
原式=[6a²b÷(-3a²)]+(5a²c²÷3a²)
=[6÷(-3)]×(a²÷a²)×b+(5÷3)×(a²÷a²)×c²
=-2×1×b+(5/3)×1×c²
=-2b+(5/3)c²

解3题
原式=16x^4÷x+4x²÷x+x÷x
=16x^(4-1)+4x^(2-1)+1
=16x³+4x+1

解4题
原式=3a²b÷ab-2ab÷ab+2ab²÷ab
=3×(a²÷a)×(b÷b)-2×(ab÷ab)+2×(a÷a)×(b²÷b)
=3a^(2-1)×1-2×1+2×1×b^(2-1)
=3a-2+2b

解5题
原式=-4a³÷(-4a²)+6a²b³÷(-4a²)+3a³b³÷(-4a²)
=[-4÷(-4)]×(a³÷a²)+[6÷(-4)]×(a²÷a²)×b³+[3÷(-4)]×(a³÷a²)×b³
=1×a^(3-2)+(-3/2)×1×b³+(-3/4)×a^(3-2)×b³
=a-(3/2)b³-(3/4)ab³

解6题
原式=(2/5mn³÷2/3n²)-(m²n²÷2/3n²)+(1/6n^4÷2/3n²)
=(2/5÷2/3)×m×(n³÷n²)-(1÷2/3)×m²×(n²÷n²)+(1/6÷2/3)×(n^4÷n²)
=(3/5)×m×n^(3-2)-(3/2)×m²×1+(1/4)×n^(4-2)
=(3/5)mn-(3/2)m²+(1/4)n²

解7题
原式=(1/10xy²÷1/5y)+(1/4y²÷1/5y)-(1/2y÷1/5y)
=(1/10÷1/5)×x×(y²÷y)+(1/4÷1/5)×(y²÷y)-(1/2÷1/5)×(y÷y)
=(1/2)×x×y^(2-1)+(5/4)×y^(2-1)-(5/2)×1
=(1/2)xy+(5/4)y-(5/2)

解8题
原式=(x×x+x×2+1×x+1×2-2)÷x
=(x²+2x+x+2-2)÷x
=(x²+3x)÷x
=x²÷x+3x÷x
=x^(2-1)+3×(x÷x)
=x+3×1
=x+3