化简:(x^2+3x+9)/(x^3-27)+6/(9-x^2)-(x-1)/(6+2x)
来源:学生作业帮助网 编辑:作业帮 时间:2024/09/02 05:56:57
![化简:(x^2+3x+9)/(x^3-27)+6/(9-x^2)-(x-1)/(6+2x)](/uploads/image/z/552526-70-6.jpg?t=%E5%8C%96%E7%AE%80%EF%BC%9A%28x%5E2%2B3x%2B9%29%2F%28x%5E3-27%29%2B6%2F%EF%BC%889-x%5E2%29-%28x-1%29%2F%286%2B2x%29)
化简:(x^2+3x+9)/(x^3-27)+6/(9-x^2)-(x-1)/(6+2x)
化简:(x^2+3x+9)/(x^3-27)+6/(9-x^2)-(x-1)/(6+2x)
化简:(x^2+3x+9)/(x^3-27)+6/(9-x^2)-(x-1)/(6+2x)
原式=(x²+3x+9)/(x-3)(x²+3x+9)-6/(x+3)(x-3)-(x-1)/2(x+3)
=1/(x-3)-6/(x+3)(x-3)-(x-1)/2(x+3)
=(2x+6-12-x²+4x-3)/[2(x+3)(x-3)]
=-(x²-6x+9)/[2(x+3)(x-3)]
=-(x-3)²/[2(x+3)(x-3)]
=(3-x)/(2x+6)
(x^2+3x+9)/(x^3-27)+6/(9-x^2)-(x-1)/(6+2x)
=:(x^2+3x+9)/[(x-3)(x²+3x+9)]+6/(9-x^2)-(x-1)/(6+2x)
=1/(x-3)-6/[(x+3)(x-3)]-(x+1)/[2(x+3)]
=[2(x+3)-12-(x+1)(x-3)]/[2(x+3)(x-3)]
=(2x+6-12-x²+2x+3)/[2(x+3)(x-3)]
=(-x²+4x-3)/[2(x+3)(x-3)]
=-(x-3)(x-1)/[2(x+3)(x-3)]
=-(x-1)/[2(x+3)]
(x^2+3x+9)/(x^3-27)+6/(9-x^2)-(x-1)/(6+2x)=(x^2+3x+9)/(x-3)(x²+3x+9)+6/(3-x)(3+x)-(x-1)/2(3+x)=
(12-6-2x+(x-1)(3-x))/2(3-x)(3+x)=(x+1)/2(x+3)