总述：本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业：求方程 4 = (x/(x+1))+((x+1)/(x+2))+((x+2)/(x+3))+((x+3)/(x+4)) 的解.
题型：方程
解:原方程：| | 4 | = | ( | x | ÷ | ( | x | + | 1 | ) | ) | + | ( | ( | x | + | 1 | ) | ÷ | ( | x | + | 2 | ) | ) | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | + | ( | ( | x | + | 3 | ) | ÷ | ( | x | + | 4 | ) | ) |
去掉方程右边的一个括号：
| | 4 | = | x | ÷ | ( | x | + | 1 | ) | + | ( | ( | x | + | 1 | ) | ÷ | ( | x | + | 2 | ) | ) | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | + | ( | ( | x | + | 3 | ) | ÷ | ( | x | + | 4 | ) | ) |
| | 4 | ( | x | + | 1 | ) | = | x | + | ( | ( | x | + | 1 | ) | ÷ | ( | x | + | 2 | ) | ) | ( | x | + | 1 | ) | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | ( | x | + | 1 | ) | + | ( | ( | x | + | 3 | ) | ÷ | ( | x | + | 4 | ) | ) | ( | x | + | 1 | ) |
去掉方程左边的一个括号：
| | 4 | x | + | 4 | × | 1 | = | x | + | ( | ( | x | + | 1 | ) | ÷ | ( | x | + | 2 | ) | ) | ( | x | + | 1 | ) | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | ( | x | + | 1 | ) | + | ( | ( | x | + | 3 | ) | ÷ | ( | x | + | 4 | ) | ) | ( | x | + | 1 | ) |
去掉方程右边的一个括号：
| | 4 | x | + | 4 | × | 1 | = | x | + | ( | x | + | 1 | ) | ÷ | ( | x | + | 2 | ) | × | ( | x | + | 1 | ) | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | ( | x | + | 1 | ) | + | ( | ( | x | + | 3 | ) | ÷ | ( | x | + | 4 | ) | ) | ( | x | + | 1 | ) |
方程化简为：
| | 4 | x | + | 4 | = | x | + | ( | x | + | 1 | ) | ÷ | ( | x | + | 2 | ) | × | ( | x | + | 1 | ) | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | ( | x | + | 1 | ) | + | ( | ( | x | + | 3 | ) | ÷ | ( | x | + | 4 | ) | ) | ( | x | + | 1 | ) |
| | 4 | x | ( | x | + | 2 | ) | + | 4 | ( | x | + | 2 | ) | = | x | ( | x | + | 2 | ) | + | ( | x | + | 1 | ) | ( | x | + | 1 | ) | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | ( | x | + | 1 | ) | ( | x | + | 2 | ) | + | ( | ( | x | + | 3 | ) | ÷ | ( | x | + | 4 | ) | ) | ( | x | + | 1 | ) | ( | x | + | 2 | ) |
去掉方程左边的一个括号：
| | 4 | x | x | + | 4 | x | × | 2 | + | 4 | ( | x | + | 2 | ) | = | x | ( | x | + | 2 | ) | + | ( | x | + | 1 | ) | ( | x | + | 1 | ) | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | ( | x | + | 1 | ) | ( | x | + | 2 | ) | + | ( | ( | x | + | 3 | ) | ÷ | ( | x | + | 4 | ) | ) | ( | x | + | 1 | ) | ( | x | + | 2 | ) |
去掉方程右边的一个括号：
| | 4 | x | x | + | 4 | x | × | 2 | + | 4 | ( | x | + | 2 | ) | = | x | x | + | x | × | 2 | + | ( | x | + | 1 | ) | ( | x | + | 1 | ) | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | ( | x | + | 1 | ) | ( | x | + | 2 | ) | + | ( | ( | x | + | 3 | ) | ÷ | ( | x | + | 4 | ) | ) | ( | x | + | 1 | ) | ( | x | + | 2 | ) |
方程化简为：
| | 4 | x | x | + | 8 | x | + | 4 | ( | x | + | 2 | ) | = | x | x | + | x | × | 2 | + | ( | x | + | 1 | ) | ( | x | + | 1 | ) | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | ( | x | + | 1 | ) | ( | x | + | 2 | ) | + | ( | ( | x | + | 3 | ) | ÷ | ( | x | + | 4 | ) | ) | ( | x | + | 1 | ) | ( | x | + | 2 | ) |
去掉方程左边的一个括号：
| | 4 | x | x | + | 8 | x | + | 4 | x | + | 4 | × | 2 | = | x | x | + | 2 | x | + | ( | x | + | 1 | ) | ( | x | + | 1 | ) | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | ( | x | + | 1 | ) | ( | x | + | 2 | ) | + | ( | ( | x | + | 3 | ) | ÷ | ( | x | + | 4 | ) | ) | ( | x | + | 1 | ) | ( | x | + | 2 | ) |
去掉方程右边的一个括号：
| | 4 | x | x | + | 8 | x | + | 4 | x | + | 4 | × | 2 | = | x | x | + | 2 | x | + | x | ( | x | + | 1 | ) | + | 1 | ( | x | + | 1 | ) | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | ( | x | + | 1 | ) | ( | x | + | 2 | ) | + | ( | ( | x | + | 3 | ) | ÷ | ( | x | + | 4 | ) | ) |
方程化简为：
| | 4 | x | x | + | 8 | x | + | 4 | x | + | 8 | = | x | x | + | 2 | x | + | x | ( | x | + | 1 | ) | + | 1 | ( | x | + | 1 | ) | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | ( | x | + | 1 | ) | ( | x | + | 2 | ) | + | ( | ( | x | + | 3 | ) | ÷ | ( | x | + | 4 | ) | ) |
方程化简为：
| | 4 | x | x | + | 12 | x | + | 8 | = | x | x | + | 2 | x | + | x | ( | x | + | 1 | ) | + | 1 | ( | x | + | 1 | ) | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | ( | x | + | 1 | ) | ( | x | + | 2 | ) | + | ( | ( | x | + | 3 | ) | ÷ | ( | x | + | 4 | ) | ) |
去掉方程右边的一个括号：
| | 4 | x | x | + | 12 | x | + | 8 | = | x | x | + | 2 | x | + | x | x | + | x | × | 1 | + | 1 | ( | x | + | 1 | ) | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | ( | x | + | 1 | ) |
方程化简为：
| | 4 | x | x | + | 12 | x | + | 8 | = | x | x | + | 3 | x | + | x | x | + | 1 | ( | x | + | 1 | ) | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | ( | x | + | 1 | ) | ( | x | + | 2 | ) | + | ( | ( | x | + | 3 | ) | ÷ | ( | x | + | 4 | ) | ) |
去掉方程右边的一个括号：
| | 4 | x | x | + | 12 | x | + | 8 | = | x | x | + | 3 | x | + | x | x | + | 1 | x | + | 1 | × | 1 | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | ( | x | + | 1 | ) |
方程化简为：
| | 4 | x | x | + | 12 | x | + | 8 | = | x | x | + | 3 | x | + | x | x | + | 1 | x | + | 1 | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | ( | x | + | 1 | ) | ( | x | + | 2 | ) |
方程化简为：
| | 4 | x | x | + | 12 | x | + | 8 | = | x | x | + | 4 | x | + | x | x | + | 1 | + | ( | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | ) | ( | x | + | 1 | ) | ( | x | + | 2 | ) | + | ( | ( | x | + | 3 | ) | ÷ | ( | x | + | 4 | ) | ) | ( | x | + | 1 | ) |
去掉方程右边的一个括号：
| | 4 | x | x | + | 12 | x | + | 8 | = | x | x | + | 4 | x | + | x | x | + | 1 | + | ( | x | + | 2 | ) | ÷ | ( | x | + | 3 | ) | × | ( | x | + | 1 | ) | ( | x | + | 2 | ) | + | ( | ( | x | + | 3 | ) | ÷ | ( | x | + | 4 | ) | ) |
| | 4 | x | x | ( | x | + | 3 | ) | + | 12 | x | ( | x | + | 3 | ) | + | 8 | ( | x | + | 3 | ) | = | x | x | ( | x | + | 3 | ) | + | 4 | x | ( | x | + | 3 | ) | + | x | x | ( | x | + | 3 | ) | + | 1 | ( | x | + | 3 | ) | + | ( | x | + | 2 | ) |
去掉方程左边的一个括号：
| | 4 | x | x | x | + | 4 | x | x | × | 3 | + | 12 | x | ( | x | + | 3 | ) | + | 8 | = | x | x | ( | x | + | 3 | ) | + | 4 | x | ( | x | + | 3 | ) | + | x | x | ( | x | + | 3 | ) | + | 1 | ( | x | + | 3 | ) | + | ( | x | + | 2 | ) |
去掉方程右边的一个括号：
| | 4 | x | x | x | + | 4 | x | x | × | 3 | + | 12 | x | ( | x | + | 3 | ) | + | 8 | = | x | x | x | + | x | x | × | 3 | + | 4 | x | ( | x | + | 3 | ) | + | x | x | ( | x | + | 3 | ) |
方程化为一般式后，有公因式：
( 2x + 5 )
由
2x + 5 = 0
得：
不能由因式分解法得出的解：
x2≈-3.618034 ，保留6位小数
x3≈-1.381966 ，保留6位小数
有 3个解。
解程的详细方法请参阅：《方程的解法》
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