在线解一元方程：
直接输入任意的一元方程，然后点击“下一步”按钮，即可获得方程的解。
它支持包含数学函数的方程。
直接输入任意的一元方程，然后点击“下一步”按钮，即可获得方程的解。
它支持包含数学函数的方程。
总述：本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业：求方程 (2/3-x)/(1+(2/3)×x) = (3/2-2/3)/(1+(3/2)×(2/3)) 的解.
题型：方程
解:原方程：
| ( | 2 | ÷ | 3 | − | x | ) | ÷ | ( | 1 | + | ( | 2 | ÷ | 3 | ) | x | ) | = | ( | 3 | ÷ | 2 | − | 2 | ÷ | 3 | ) | ÷ | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) |
| 方程两边同时乘以： | ( | 1 | + | ( | 2 | ÷ | 3 | ) | x | ) | , | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) |
| ( | 2 | ÷ | 3 | − | x | ) | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) | = | ( | 3 | ÷ | 2 | − | 2 | ÷ | 3 | ) | ( | 1 | + | ( | 2 | ÷ | 3 | ) | x | ) |
| 2 | ÷ | 3 | × | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) | − | x | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) | = | ( | 3 | ÷ | 2 | − | 2 | ÷ | 3 | ) | ( | 1 | + | ( | 2 | ÷ | 3 | ) | x | ) |
| 2 | ÷ | 3 | × | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) | − | x | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) | = | 3 | ÷ | 2 | × | ( | 1 | + | ( | 2 | ÷ | 3 | ) | x | ) | − | 2 | ÷ | 3 | × | ( | 1 | + | ( | 2 | ÷ | 3 | ) | x | ) |
2 3 | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) | − | x | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) | = | 3 2 | ( | 1 | + | ( | 2 | ÷ | 3 | ) | x | ) | − | 2 3 | ( | 1 | + | ( | 2 | ÷ | 3 | ) | x | ) |
2 3 | × | 1 | + | 2 3 | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | − | x | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) | = | 3 2 | ( | 1 | + | ( | 2 | ÷ | 3 | ) | x | ) | − | 2 3 | ( | 1 | + | ( | 2 | ÷ | 3 | ) | x | ) |
2 3 | × | 1 | + | 2 3 | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | − | x | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) | = | 3 2 | × | 1 | + | 3 2 | ( | 2 | ÷ | 3 | ) | x | − | 2 3 | ( | 1 | + | ( | 2 | ÷ | 3 | ) | x | ) |
2 3 | + | 2 3 | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | − | x | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) | = | 3 2 | + | 3 2 | ( | 2 | ÷ | 3 | ) | x | − | 2 3 | ( | 1 | + | ( | 2 | ÷ | 3 | ) | x | ) |
2 3 | + | 2 3 | × | 3 | ÷ | 2 | × | ( | 2 | ÷ | 3 | ) | − | x | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) | = | 3 2 | + | 3 2 | ( | 2 | ÷ | 3 | ) | x | − | 2 3 | ( | 1 | + | ( | 2 | ÷ | 3 | ) | x | ) |
2 3 | + | 2 3 | × | 3 | ÷ | 2 | × | ( | 2 | ÷ | 3 | ) | − | x | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) | = | 3 2 | + | 3 2 | × | 2 | ÷ | 3 | × | x | − | 2 3 | ( | 1 | + | ( | 2 | ÷ | 3 | ) | x | ) |
2 3 | + | 1 | ( | 2 | ÷ | 3 | ) | − | x | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) | = | 3 2 | + | 1 | x | − | 2 3 | ( | 1 | + | ( | 2 | ÷ | 3 | ) | x | ) |
2 3 | + | 1 | × | 2 | ÷ | 3 | − | x | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) | = | 3 2 | + | 1 | x | − | 2 3 | ( | 1 | + | ( | 2 | ÷ | 3 | ) | x | ) |
2 3 | + | 1 | × | 2 | ÷ | 3 | − | x | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) | = | 3 2 | + | 1 | x | − | 2 3 | × | 1 | − | 2 3 | ( | 2 | ÷ | 3 | ) | x |
2 3 | + | 2 3 | − | x | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) | = | 3 2 | + | 1 | x | − | 2 3 | − | 2 3 | ( | 2 | ÷ | 3 | ) | x |
4 3 | − | x | ( | 1 | + | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | ) | = | 5 6 | + | 1 | x | − | 2 3 | ( | 2 | ÷ | 3 | ) | x |
4 3 | − | x | × | 1 | − | x | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | = | 5 6 | + | 1 | x | − | 2 3 | ( | 2 | ÷ | 3 | ) | x |
4 3 | − | x | × | 1 | − | x | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | = | 5 6 | + | 1 | x | − | 2 3 | × | 2 | ÷ | 3 | × | x |
4 3 | − | x | × | 1 | − | x | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | = | 5 6 | + | 1 | x | − | 4 9 | x |
4 3 | − | 1 | x | − | x | ( | 3 | ÷ | 2 | ) | ( | 2 | ÷ | 3 | ) | = | 5 6 | + | 5 9 | x |
4 3 | − | 1 | x | − | x | × | 3 | ÷ | 2 | × | ( | 2 | ÷ | 3 | ) | = | 5 6 | + | 5 9 | x |
4 3 | − | 1 | x | − | x | × | 3 2 | ( | 2 | ÷ | 3 | ) | = | 5 6 | + | 5 9 | x |
4 3 | − | 1 | x | − | x | × | 3 2 | × | 2 | ÷ | 3 | = | 5 6 | + | 5 9 | x |
4 3 | − | 1 | x | − | x | × | 1 | = | 5 6 | + | 5 9 | x |
4 3 | − | 2 | x | = | 5 6 | + | 5 9 | x |
移项：即，把含有未知数的项移到方程左边，把只含有常数的项移到方程的右边。
注意，移项时，该项前面的正负号要改变，即，正号变为负号，而负号要改变为正号。这与方程两边同时加上或者减去该项是等价的。
| - | 2 | x | − | 5 9 | x | = | 5 6 | − | 4 3 |
合并方程左边含有未知数的各项：
| - | 23 9 | x | = | 5 6 | − | 4 3 |
合并方程右边的各项：
| - | 23 9 | x | = | - | 1 2 |
方程两边同时移项，改变符号 得：
1 2 | = | 23 9 | x |
方程的左边等于右边，则右边也 一定等于左边，即：
23 9 | x | = | 1 2 |
把未知数的系数化为 1：
| x | = | 1 2 | ÷ | 23 9 |
| = | 1 2 | × | 9 23 |
得：
| x | = | 9 46 |
把结果化为小数形式：
| x | = | 0.195652 |
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