From d4c6f52f4a9ba1a2c6ef51d6f8c64063bd1cda81 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E8=B5=B5=E9=91=AB?= <7176466@qq.com>
Date: Thu, 18 Aug 2022 18:15:37 +0800
Subject: [PATCH] =?UTF-8?q?=E5=B0=8F=E4=BF=AE=E6=94=B9?=
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---
 知识点/除法.md |  4 +++-
 问题/均贫富.md | 10 +++++++++-
 2 files changed, 12 insertions(+), 2 deletions(-)

diff --git a/知识点/除法.md b/知识点/除法.md
index 74abf03..4384b08 100644
--- a/知识点/除法.md
+++ b/知识点/除法.md
@@ -1,7 +1,9 @@
 # 除法
 
-$\forall (a,b,x,y)\in\mathbb{Z} \land x\neq0, y={a}{x}+b \iff {y}\div{x}={a}\cdots{b}$
+$\forall (a,b,y)\in\mathbb{N}, x\in \Bbb{Z^+}, {y}\div{x}={a}\cdots{b} \iff y={a}{x}+b$
 
 $y$称为<u>被除数</u>，$x$称为<u>除数</u>，$a$称为<u>商</u>，$b$称为<u>余数</u>
 
 当$b=0$时称$y$整除$x$，或称$y$是$x$的倍数。此时有$y\div{x}=a \Longrightarrow y\div{a}=x$。
+
+**如何实现MathJax输入除法竖式？**
diff --git a/问题/均贫富.md b/问题/均贫富.md
index 7bcbb83..244e8a7 100644
--- a/问题/均贫富.md
+++ b/问题/均贫富.md
@@ -9,7 +9,11 @@
 $
 \begin{aligned}
 a - x &= b + x &({a}\in\Bbb{N},{b}\in\Bbb{N},a>b) \\\\
-2x &= a - b  &(移项并交换等式两侧) \\\\
+a - x + x &= b + 2x &(等式两侧同加x) \\\\
+a &= b + 2x  \\\\
+a - b &= b -b+ 2x &(等式两侧同减b) \\\\
+a -b &= 2x  \\\\
+2x &= a - b  &(交换等式两侧) \\\\
  x &= \dfrac{a-b}{2}  &(等式两侧同除以2)
 \end{aligned}
 $
@@ -17,3 +21,7 @@ $
 ## 解法2
 
 $ x = \dfrac{a+b}{2} - b $
+
+## 其实两个解法的结果是一样的
+
+$\dfrac{a+b}{2} - b= \dfrac{a+b}{2}-\dfrac{2b}{2} = \dfrac{a+b-2b}{2} = \dfrac{a-b}{2}$