总述：本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业：求方程 20((X+1+5/4)/(2/(2/5)))/(2/3) = ((3-1)(1/(1/2))+1)/(1/(1+4)) 的解.
题型：方程
解:原方程：| | 20 | ( | ( | X | + | 1 | + | 5 | ÷ | 4 | ) | ÷ | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | ) | ÷ | ( | 2 | ÷ | 3 | ) | = | ( | ( | 3 | − | 1 | ) | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | + | 1 | ) | ÷ | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) |
| 方程两边同时乘以： | ( | 2 | ÷ | 3 | ) | , | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) |
| | 20 | ( | ( | X | + | 1 | + | 5 | ÷ | 4 | ) | ÷ | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | ) | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | = | ( | ( | 3 | − | 1 | ) | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | + | 1 | ) | ( | 2 | ÷ | 3 | ) |
去掉方程左边的一个括号：
| | 20 | ( | X | + | 1 | + | 5 | ÷ | 4 | ) | ÷ | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | × | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | = | ( | ( | 3 | − | 1 | ) | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | + | 1 | ) | ( | 2 | ÷ | 3 | ) |
去掉方程右边的一个括号：
| | 20 | ( | X | + | 1 | + | 5 | ÷ | 4 | ) | ÷ | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | × | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | = | ( | 3 | − | 1 | ) | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | + | 1 | ( | 2 | ÷ | 3 | ) |
| | 20 | ( | X | + | 1 | + | 5 | ÷ | 4 | ) | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | = | ( | 3 | − | 1 | ) | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | + | 1 | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) |
去掉方程左边的一个括号：
| | 20 | X | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | + | 20 | × | 1 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | + | 20 | × | 5 | ÷ | 4 | × | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | = | ( | 3 | − | 1 | ) | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | + | 1 | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) |
去掉方程右边的一个括号：
| | 20 | X | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | + | 20 | × | 1 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | + | 20 | × | 5 | ÷ | 4 | × | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | = | 3 | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | − | 1 | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | + | 1 | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) |
方程化简为：
| | 20 | X | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | + | 20 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | + | 25 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | = | 3 | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | − | 1 | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | + | 1 | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) |
去掉方程左边的一个括号：
| | 20 | X | × | 1 | ÷ | ( | 1 | + | 4 | ) | + | 20 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | + | 25 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | = | 3 | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | − | 1 | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | + | 1 | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) |
去掉方程右边的一个括号：
| | 20 | X | × | 1 | ÷ | ( | 1 | + | 4 | ) | + | 20 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | + | 25 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | = | 3 | × | 1 | ÷ | ( | 1 | ÷ | 2 | ) | × | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | − | 1 | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | + | 1 | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) |
方程化简为：
| | 20 | X | ÷ | ( | 1 | + | 4 | ) | + | 20 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | + | 25 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | = | 3 | ÷ | ( | 1 | ÷ | 2 | ) | × | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | − | 1 | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | + | 1 | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) |
| 方程两边同时乘以： | ( | 1 | + | 4 | ) | , | ( | 1 | ÷ | 2 | ) |
| | 20 | X | ( | 1 | ÷ | 2 | ) | + | 20 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | + | 25 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | = | 3 | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | ( | 1 | + | 4 | ) | − | 1 | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | + | 1 | ( | 2 | ÷ | 3 | ) |
去掉方程左边的一个括号：
| | 20 | X | × | 1 | ÷ | 2 | + | 20 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | + | 25 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | = | 3 | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | ( | 1 | + | 4 | ) | − | 1 | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | + | 1 | ( | 2 | ÷ | 3 | ) |
去掉方程右边的一个括号：
| | 20 | X | × | 1 | ÷ | 2 | + | 20 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | + | 25 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | = | 3 | × | 2 | ÷ | 3 | × | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | ( | 1 | + | 4 | ) | − | 1 | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | + | 1 |
方程化简为：
| | 10 | X | + | 20 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | + | 25 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | = | 2 | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | ( | 1 | + | 4 | ) | − | 1 | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | + | 1 | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) |
去掉方程左边的一个括号：
| | 10 | X | + | 20 | × | 1 | ÷ | ( | 1 | + | 4 | ) | × | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | + | 25 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | = | 2 | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | ( | 1 | + | 4 | ) | − | 1 | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | + | 1 | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) |
去掉方程右边的一个括号：
| | 10 | X | + | 20 | × | 1 | ÷ | ( | 1 | + | 4 | ) | × | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | + | 25 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | = | 2 | × | 2 | ÷ | ( | 2 | ÷ | 5 | ) | × | ( | 1 | + | 4 | ) | − | 1 | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | + | 1 | ( | 2 | ÷ | 3 | ) |
方程化简为：
| | 10 | X | + | 20 | ÷ | ( | 1 | + | 4 | ) | × | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | + | 25 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | = | 4 | ÷ | ( | 2 | ÷ | 5 | ) | × | ( | 1 | + | 4 | ) | − | 1 | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | + | 1 | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) |
| 方程两边同时乘以： | ( | 1 | + | 4 | ) | , | ( | 2 | ÷ | 5 | ) |
| | 10 | X | ( | 1 | + | 4 | ) | ( | 2 | ÷ | 5 | ) | + | 20 | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | ( | 2 | ÷ | 5 | ) | + | 25 | ( | 1 | ÷ | ( | 1 | + | 4 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | = | 4 | ( | 1 | + | 4 | ) | ( | 1 | + | 4 | ) | − | 1 | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | ( | 1 | + | 4 | ) | ( | 2 | ÷ | 5 | ) | + | 1 |
去掉方程左边的一个括号：
| | 10 | X | × | 1 | ( | 2 | ÷ | 5 | ) | + | 10 | X | × | 4 | ( | 2 | ÷ | 5 | ) | + | 20 | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | ( | 2 | ÷ | 5 | ) | = | 4 | ( | 1 | + | 4 | ) | ( | 1 | + | 4 | ) | − | 1 | ( | 1 | ÷ | ( | 1 | ÷ | 2 | ) | ) | ( | 2 | ÷ | 3 | ) | ( | 2 | ÷ | ( | 2 | ÷ | 5 | ) | ) | ( | 1 | + | 4 | ) | ( | 1 | ÷ | 2 | ) | ( | 1 | + | 4 | ) | ( | 2 | ÷ | 5 | ) | + | 1 |
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