1.(x^2+6x^3-10x+4)/(2x-1)
=[(6x^3-3x^2)+(4x^2-2x)-(8x-4)]/(2x-1)
=(2x-1)(3x^2+2x-1)/(2x-1)
=3x^2+2x-1
2.（5x^2+2x^3-1)/(2x+1)
=[(2x^3+x^2)+(4x^2-1)]/(2x+1)
=(2x+1)(x^2+2x-1)/(2x+1)
=x^2+2x-1
3.(x^5-1)/(x-1)
=[(x^5-x^4)+(x^4-x^3)+(x^3-x^2)+(x^2-x)+(x-1)]/(x-1)
=(x-1)(x^4+x^3+x^2+x+1)/(x-1)
=x^4+x^3+x^2+x+1
4.(2x^3+9x^2+3x+5)/(x^2+4x-3)
=[(2x^3+8x^2-6x)+(x^2+4x-3)+(5x+8)]/(x^2+4x-3)
=(2x+1)+(5x+8)/(x^2+4x-3)
5.(9x^2+2x^3+5)/(4x-3+x^2)
=[(2x^3+8x^2-6x)+(x^2+4x-3)+(2x+8)]/(4x-3+x^2)
=(2x1)+(2x+8)/(4x-3+x^2)
6.(x^10+x^5+1)/(x^2+x+1)
=[(x^10+x^9+x^8)-(x^9+x^8+x^7)+(x^7+x^6+x^5)-(x^6+x^5+x^4)+(x^5+x^4+x^3)-(x^3+x^2+x^2)+(x^2+x+1)]/(x^2+x+1)
=(x^2+x+1)(x^8-x^7+x^5-x^4+x^3-x^2+1)/(x^2+x+1)
=x^8-x^7+x^5-x^4+x^3-x^2+1
7.(3a^5-2a^4b-7a^3b^2+7a^2b^3-b^5)/(a+b)
=[(3a^5+3a^4b)-(5a^4b+5a^3b^2)-(2a^3b^2+2a^2b^3)+(9a^2b^3+9ab^4)-(9ab^4+9b^5)+9b^5]/(a+b)
=(3a^4-5a^3b-2a^2b^2+9ab^3-9b^4)+9b^5/(a+b)