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先把视频暂停一下，自己想想怎么做

2
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这2个有理式的加法

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好了，我想您有自己的解决方法

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我们现在来一起做这道题

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第一个要考虑的事情我们

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00:00:10,777 --> 00:00:12,101
就是您在做这个题的时候

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您要意识到它们有不同的分母

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而把分数式加起来很难的

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当它们有不同的分母的时候

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00:00:17,766 --> 00:00:18,695
您必须重写它们

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让它们有共同的分母

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最简单的方法获取共同的分母

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就是把2个不同的分母相乘

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特别是遇到像这样的2个分母

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它们之间没有共同的因子

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它们本身就是一个因子

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它们之间没有任何共同的因子

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那我们就来建立这个共同的分母吧

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所以它应该等于

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它应该等于什么呢

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让我们想想，它应该等于

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我们共同的分母

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让我来写下来

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先来写下2x

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我用另一个颜色来表示吧

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所以我们用(2x-3）

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乘以(3x+1)

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乘以(3x+1)

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然后加上

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加上下面的式子

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同样的分母为(2x-3）

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(2x-3）

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乘以(3x+1)

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乘以(3x+1)

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那么第一个式子里分母从2x

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从(2x-3)变成现在的分母

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（2x-3)乘以(3x+1)

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我们在之前的分母上乘以了(3x+1)

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那么如果我们在分母上乘上什么数

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而我们并不想改变这个分数的值

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也就是这个有理式的值

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我们也需要在分子上乘以同样的数

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之前的分子是5x

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我用蓝色来表示

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所以说之前的分子是5x

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我们也要用它来乘以(3x+1)

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来乘以(3x+1)

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大家注意我并没有改变这个分数的值

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我是在分子分母上同时乘以(3x+1)

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只要(3x+1)不等于0这个式子就成立

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我们又用同样的方法来做另一个

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这个式子的分母是(3x+1)

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我们来乘以(2x-3)

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所以我要用之前的分子

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也就是-4x²

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也要来乘以(2x-3)

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写下(2x-3)

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我把圆括号加上

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这样就不会看起来减去4x²

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好了，我们现在可以重新写了

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它们就等于

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分母上

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在分子上，5x乘以3x

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就等于15x²

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5x乘以1， 就是加上5x

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我们再来看

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我现在用绿色

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我可以用负4x乘以2x

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应该得到负的8x²

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然后负的4x乘以负3

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变成正的12x²

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我做对了吗

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负的

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喔，我要特别小心

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我的直觉告诉我，我可能哪里做错了

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实际上，如果您把视频暂停一下，您可以发现

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我在哪里做错了

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负的4x²乘以2x

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是变成负8的x的立方

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- 8x³

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然后负4x²乘以负3应该等于负12x²

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这里我们整个的分母

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整个分母

84
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我们有一个共同的分母

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所以我们分子可以全部加起来

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分母就是(2x-3)

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(2x-3)

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乘以(3x+1)

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乘以(3x+1)

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现在我们来看这么简化它

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整个式子就应该变成

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让我来画出来

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我们要确定的是这是一个优理式

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让我们来看看

95
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我们这里最高的方次向是负的8x³

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我们写下来负8

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负8x³

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然后我们有15x²

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我们还有12x²

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我们可以把这2项加起来

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得到27x²

102
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好了，我们已经做好这个

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绿色部分我们已经完成

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我们已经做好

105
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我们已经做好这2部分，现在还剩下5x

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那就把加5x写下

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然后这就是整个分子

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分母呢，就是(2x-3) 乘以(3x+1)

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乘以3x+1

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现在我们

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做完了

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看起来好像

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不能再往下简化了

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当然你可以把分子的x提出来放在括弧前面

115
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但是也并不能抵减任何项

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不能与分母的任何项相抵减

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看起来我们就完成了