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 10×((1/(x))+(1/(x+4)))+(1/(((x)/2)+2)) = 1 的解.
题型：方程
解:原方程：
| 10 | ( | ( | 1 | ÷ | ( | x | ) | ) | + | ( | 1 | ÷ | ( | x | + | 4 | ) | ) | ) | + | ( | 1 | ÷ | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | ) | = | 1 |
| 10 | ( | 1 | ÷ | ( | x | ) | ) | + | 10 | ( | 1 | ÷ | ( | x | + | 4 | ) | ) | + | ( | 1 | ÷ | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | ) | = | 1 |
| 10 | × | 1 | ÷ | ( | x | ) | + | 10 | ( | 1 | ÷ | ( | x | + | 4 | ) | ) | + | ( | 1 | ÷ | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | ) | = | 1 |
| 10 | ÷ | ( | x | ) | + | 10 | ( | 1 | ÷ | ( | x | + | 4 | ) | ) | + | ( | 1 | ÷ | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | ) | = | 1 |
| 方程两边同时乘以： | ( | x | ) |
| 10 | + | 10 | ( | 1 | ÷ | ( | x | + | 4 | ) | ) | ( | x | ) | + | ( | 1 | ÷ | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | ) | ( | x | ) | = | 1 | ( | x | ) |
| 10 | + | 10 | × | 1 | ÷ | ( | x | + | 4 | ) | × | ( | x | ) | + | ( | 1 | ÷ | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | ) | ( | x | ) | = | 1 | ( | x | ) |
| 10 | + | 10 | × | 1 | ÷ | ( | x | + | 4 | ) | × | ( | x | ) | + | ( | 1 | ÷ | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | ) | ( | x | ) | = | 1 | x |
| 10 | + | 10 | ÷ | ( | x | + | 4 | ) | × | ( | x | ) | + | ( | 1 | ÷ | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | ) | ( | x | ) | = | 1 | x |
| 方程两边同时乘以： | ( | x | + | 4 | ) |
| 10 | ( | x | + | 4 | ) | + | 10 | ( | x | ) | + | ( | 1 | ÷ | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | ) | ( | x | ) | ( | x | + | 4 | ) | = | 1 | x | ( | x | + | 4 | ) |
| 10 | x | + | 10 | × | 4 | + | 10 | ( | x | ) | + | ( | 1 | ÷ | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | ) | ( | x | ) | ( | x | + | 4 | ) | = | 1 | x | ( | x | + | 4 | ) |
| 10 | x | + | 10 | × | 4 | + | 10 | ( | x | ) | + | ( | 1 | ÷ | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | ) | ( | x | ) | ( | x | + | 4 | ) | = | 1 | x | x | + | 1 | x | × | 4 |
| 10 | x | + | 40 | + | 10 | ( | x | ) | + | ( | 1 | ÷ | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | ) | ( | x | ) | ( | x | + | 4 | ) | = | 1 | x | x | + | 4 | x |
| 10 | x | + | 40 | + | 10 | x | + | ( | 1 | ÷ | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | ) | ( | x | ) | ( | x | + | 4 | ) | = | 1 | x | x | + | 4 | x |
| 20 | x | + | 40 | + | ( | 1 | ÷ | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | ) | ( | x | ) | ( | x | + | 4 | ) | = | 1 | x | x | + | 4 | x |
| 20 | x | + | 40 | + | 1 | ÷ | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | × | ( | x | ) | ( | x | + | 4 | ) | = | 1 | x | x | + | 4 | x |
| 方程两边同时乘以： | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) |
| 20 | x | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | + | 40 | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | + | 1 | ( | x | ) | ( | x | + | 4 | ) | = | 1 | x | x | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | + | 4 | x | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) |
| 20 | x | ( | ( | x | ) | ÷ | 2 | ) | + | 20 | x | × | 2 | + | 40 | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | + | 1 | ( | x | ) | ( | x | + | 4 | ) | = | 1 | x | x | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | + | 4 | x | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) |
| 20 | x | ( | ( | x | ) | ÷ | 2 | ) | + | 20 | x | × | 2 | + | 40 | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | + | 1 | ( | x | ) | ( | x | + | 4 | ) | = | 1 | x | x | ( | ( | x | ) | ÷ | 2 | ) | + | 1 | x | x | × | 2 | + | 4 | x | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) |
| 20 | x | ( | ( | x | ) | ÷ | 2 | ) | + | 40 | x | + | 40 | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | + | 1 | ( | x | ) | ( | x | + | 4 | ) | = | 1 | x | x | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | x | x | + | 4 | x | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) |
| 20 | x | ( | x | ) | ÷ | 2 | + | 40 | x | + | 40 | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | + | 1 | ( | x | ) | ( | x | + | 4 | ) | = | 1 | x | x | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | x | x | + | 4 | x | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) |
| 20 | x | ( | x | ) | ÷ | 2 | + | 40 | x | + | 40 | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | + | 1 | ( | x | ) | ( | x | + | 4 | ) | = | 1 | x | x | ( | x | ) | ÷ | 2 | + | 2 | x | x | + | 4 | x | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) |
| 10 | x | ( | x | ) | + | 40 | x | + | 40 | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | + | 1 | ( | x | ) | ( | x | + | 4 | ) | = | 1 2 | x | x | ( | x | ) | + | 2 | x | x | + | 4 | x | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) |
| 10 | x | x | + | 40 | x | + | 40 | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) | + | 1 | ( | x | ) | ( | x | + | 4 | ) | = | 1 2 | x | x | ( | x | ) | + | 2 | x | x | + | 4 | x | ( | ( | ( | x | ) | ÷ | 2 | ) | + | 2 | ) |
方程化为一般式后，用因式分解法化为：
( x + 2 )( x - 20 )=0
由
x + 2 = 0
x - 20 = 0
得：
x1=-2
x2=20
有 2个解。
解一元二次方程的详细方法请参阅：《一元二次方程的解法》
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