作业帮计算题:(3x^2+14x+16)/(x+3)-(2x^2-10x+13)/(x-3)-(x^3-9x^2-9x+75)/(x^2-9)
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/03 09:06:19
计算题:(3x^2+14x+16)/(x+3)-(2x^2-10x+13)/(x-3)-(x^3-9x^2-9x+75)/(x^2-9)
计算题:(3x^2+14x+16)/(x+3)-(2x^2-10x+13)/(x-3)-(x^3-9x^2-9x+75)/(x^2-9)
计算题:(3x^2+14x+16)/(x+3)-(2x^2-10x+13)/(x-3)-(x^3-9x^2-9x+75)/(x^2-9)
(3x^2+14x+16)/(x+3)-(2x^2-10x+13)/(x-3)-(x^3-9x^2-9x+75)/(x^2-9)
=(3x^2+9x+5x+15+1)/(x+3)-(2x^2-6x-4x+12+1)/(x-3)-(x^3-9x-9x^2+81-6)/(x^2-9)
=(3x^2+9x)/(x+3)+(5x+15)/(x+3)+1/(x+3)-[(2x^2-6x)/(x-3)-(4x-12)/(x-3)+1/(x-3)]-[(x^3-9x)/(x^2-9)-(9x^2-81)/(x^2-9)-6/(x^2-9)]
=3x(x+3)/(x+3)+5(x+3)/(x+3)+1/(x+3)-[2x(x-3)/(x-3)-4(x-3)/(x-3)+1/(x-3)]-[x(x^2-9)/(x^2-9)-9(x^2-9)/(x^2-9)-6/(x^2-9)]
=3x+5+1/(x+3)-[2x-4+1/(x-3)]-[x-9-6/(x^2-9)]
=3x+5+1/(x+3)-2x+4-1/(x-3)-x+9+6/(x^2-9)
=3x-2x-x+5+4+9+1/(x+3)-1/(x-3)+6/(x^2-9)
=18+1/(x+3)-1/(x-3)+6/(x^2-9)
=18+(x-3)/(x-3)(x+3)-(x+3)/(x-3)(x+3)+6/(x-3)(x+3)
=18+[(x-3)-(x+3)+6]/(x-3)(x+3)
=18+(x-3-x-3+6)/(x-3)(x+3)
=18
通分，分母统一变成x^2-9，后面应该就没问题了