化简:2a+b/a²-b²+b/b²-a²-2b/(a+b)(a-b).
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/17 16:13:11
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化简:2a+b/a²-b²+b/b²-a²-2b/(a+b)(a-b).
化简:2a+b/a²-b²+b/b²-a²-2b/(a+b)(a-b).
化简:2a+b/a²-b²+b/b²-a²-2b/(a+b)(a-b).
2a+b/a²-b²+b/b²-a²-2b/(a+b)(a-b).
=2a+b/(a²-b²)-b/(a²-b²)-2b/(a²-b²)
=(2a+b-b-2b)/(a-b)(a+b)
=2(a-b)/(a-b)(a+b)
=2/(a+b)
这里用到平方差公式:a²-b²=(a-b)(a+b)
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(2 a + b)/ (a ² - b ²) + b / (b ² - a ²) - 2 b / (a + b)(a - b)
= (2 a + b)/(a + b)(a - b) - b / (a + b)(a - b)- 2 b / (a + b)(a - b)
= (2 a + b - b - 2 b)/ (a + b)(a - b)<...
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(2 a + b)/ (a ² - b ²) + b / (b ² - a ²) - 2 b / (a + b)(a - b)
= (2 a + b)/(a + b)(a - b) - b / (a + b)(a - b)- 2 b / (a + b)(a - b)
= (2 a + b - b - 2 b)/ (a + b)(a - b)
= (2 a - 2 b)/ (a + b)(a - b)
= 2(a - b)/ (a + b)(a - b)
= 2 / (a + b)
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