计算:(x^2+6x+10)/(x^2+6x+9)+(x^2-11)/(x^2-9)+(2x^2+8x+5)/(x^2+
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/15 04:48:33
计算:(x^2+6x+10)/(x^2+6x+9)+(x^2-11)/(x^2-9)+(2x^2+8x+5)/(x^2+4x+3)
看三个分母的因式可以知道:
首先,每个提出一个常数,把分子化成简单的常数,即化为:
1+1/(x^2+6x+9)+1-2/(x^2-9)+2-1/(x^2+4x+3)
接着,每个因式分母提出(x+3),即为:
4+1/(x+3) * [1/(x+3)-2/(x-3)-1/(x+1)]
最后,中括号内通分化简即可:
4+1/(x+3) * [(x-3)(x+1)-2(x+3)(x-1)-(x+3)(x-3)/(x+3)(x-3)(x+1)]
=4+1/(x+3) * (x^2-2x-3-2x^2-4x+6-x^2+9)/[(x+3)(x-3)(x+1)]
=4+1/(x+3) * (-2x^2-6x+12)/[(x+3)(x-3)(x+1)]
=4-1/(x+3) * (2x^2+6x-12)/[(x+3)(x-3)(x+1)]
=4-2/(x+3) * (x-1)(x+4)/[(x+3)(x-3)(x+1)]
首先,每个提出一个常数,把分子化成简单的常数,即化为:
1+1/(x^2+6x+9)+1-2/(x^2-9)+2-1/(x^2+4x+3)
接着,每个因式分母提出(x+3),即为:
4+1/(x+3) * [1/(x+3)-2/(x-3)-1/(x+1)]
最后,中括号内通分化简即可:
4+1/(x+3) * [(x-3)(x+1)-2(x+3)(x-1)-(x+3)(x-3)/(x+3)(x-3)(x+1)]
=4+1/(x+3) * (x^2-2x-3-2x^2-4x+6-x^2+9)/[(x+3)(x-3)(x+1)]
=4+1/(x+3) * (-2x^2-6x+12)/[(x+3)(x-3)(x+1)]
=4-1/(x+3) * (2x^2+6x-12)/[(x+3)(x-3)(x+1)]
=4-2/(x+3) * (x-1)(x+4)/[(x+3)(x-3)(x+1)]
|X-1|+|X-2|+|X-3|+|X-4|+|X-5|+|X-6|+|X-7|+|X-8|+|X-9|+|X-10|
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