WEBVTT

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欢迎来到线性方程第四课

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让我们来解题吧

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首先

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假设我有一个情况——让我出几题

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——假设我有3/x等于5

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我们想要——这道题和我们以前见过的

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题目都不太一样

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因为不是在分子上有x

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我们现在是分母是x

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我自己不太喜欢分母含有x的情况

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所以我们想尽快将其

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从分母上拿出来，或者至少

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去除它

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一个将分母上的数提出来的方法是

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我们可以等式两侧同乘x

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左侧等式的两个x

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会相互抵消

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在右侧，你会得到5乘x

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这等于——两个x抵消掉

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你得到3等于5x

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现在，我们也可以将其写成5x等于3

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然后我们有两种思考方法

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我们可以两侧同时乘以1/5，或者你可以

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同除以5

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如果你两侧同乘以1/5

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左手边变成x

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右手边是3乘以1/5，等于3/5

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我们这做了什么？

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这就很快变成第二节课

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的题目，或者第一节课

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的题目

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我们只需要两侧同时

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乘以x

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我们就把x从分母上去除了

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我们再做一题

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假设我们有x加2除以x加1

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等于7

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这里的分母上不是只有x

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分母时x加1

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但我们的步骤一样

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要把x+1从分母上拿出来，我们可以

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灯饰两侧同时乘以x+1除以1

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既然我们左侧已经乘了

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右侧也得这样，就是7/1

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乘以x+1除以1

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左侧，x+1抵消

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只留下x+2

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除以1，但你可以忽略这个1

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这等于7乘以x+1

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这等于x+2

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记住，这是7乘以整个x+1

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所以我们得使用分配法则

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这等于7x加7

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现在，我们变成了一个

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三级方程

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我们现在要把所有x项

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放到等式左侧

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所有常数项，类似2和7，

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移到等式右侧

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我们首先把x移到左侧

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要把7x放到左侧

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我们可以两侧同时减7x

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负7x，加，这是负7x

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右手边，两个7x抵消

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左手边就时负7x加x

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就是负6x加2等于

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右侧剩下的7

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现在我们需要去掉2

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我们可以两侧同时减2

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剩下来的就是负6x等于5

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这是一级问题

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我们只需要两侧同时乘以

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左侧的因数的倒数

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因数是负6

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所以我们两侧同乘以负1/6

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负1/6

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左手边是负1/6乘以负6

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也就是1

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所以我们得到x等于5乘以负1/6

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就是负5/6

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题目结束

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如果你想要验算，你可以把

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x等于负5/6带回到原方程

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去检查一下是否成立

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让我们再做一题

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我临时想的题目，不好意思

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让我想想

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3乘以x加5等于8乘以x加2

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我们干同样的事

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虽然我们现在分母上有两个表达式

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我们都想提取出来

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我们想要把x+5提出来，我们想要

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把这个x+2也提出来

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首先做一下x+5

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就和之前一样，我们两侧同时

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乘以x+5

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你可以看成x+5除以1

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乘以x+5除以1

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在左侧，它们互相抵消

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剩下来的是3乘以8乘以x+5

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这个这个除以x+2

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现在，简化上面，

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我们只需要把8乘以整个表达式

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也就是8x加40除以x+2

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现在，我们去掉这个x+2

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我们用一样的方法

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我们两侧同时乘以

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x+2出1

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x+2

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我们可以看成两侧同乘

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x+2

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1是非必要的

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所以左侧变成3x加6

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记住，要把3分配进去，因为

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你是乘整个表达式

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x+2

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在右侧

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我们有x+2，和这个x+2相互抵消

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剩下来8x加40

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现在变成了三级问题

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如果我们两侧同减去8x，减8x，加——

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我觉得我没空间了

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减8x

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右侧的8x互相抵消

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左边我们有负5x加6等于

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右侧剩下的40

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现在我们可以等式两侧同减去6

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让我写出来

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减6x加负6

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现在，希望我没有太快

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你们可以跟上

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但如果我们两侧减去负6，在左边

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我们只剩下了负5x等于，

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在右边，我们有34

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现在变成了一级问题

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我们只需要两侧同时乘以负1/5

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负1/5

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在左边我们有x

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在右边我们有负34/5

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除非我大意出错，应该是对的

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我觉得你应该理解了我们这里的过程

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你现在应该准备好了解四级线性方程

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祝你好运