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 1/(x+5)+2/(x+4)-3/(x+3)-3/(x+2)+2/(x+1)+1/x = 0 的解.
题型：方程
解:原方程：
| 1 | ÷ | ( | x | + | 5 | ) | + | 2 | ÷ | ( | x | + | 4 | ) | - | 3 | ÷ | ( | x | + | 3 | ) | - | 3 | ÷ | ( | x | + | 2 | ) | + | 2 | ÷ | ( | x | + | 1 | ) | + | 1 | ÷ | x | = | 0 |
| 方程两边同时乘以： | ( | x | + | 5 | ) |
| 1 | + | 2 | ÷ | ( | x | + | 4 | ) | × | ( | x | + | 5 | ) | - | 3 | ÷ | ( | x | + | 3 | ) | × | ( | x | + | 5 | ) | - | 3 | ÷ | ( | x | + | 2 | ) | × | ( | x | + | 5 | ) | + | 2 | ÷ | ( | x | + | 1 | ) | × | ( | x | + | 5 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | = | 0 | ( | x | + | 5 | ) |
| 1 | + | 2 | ÷ | ( | x | + | 4 | ) | × | x | + | 2 | ÷ | ( | x | + | 4 | ) | × | 5 | - | 3 | ÷ | ( | x | + | 3 | ) | × | ( | x | + | 5 | ) | - | 3 | ÷ | ( | x | + | 2 | ) | × | ( | x | + | 5 | ) | + | 2 | ÷ | ( | x | + | 1 | ) | × | ( | x | + | 5 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | = | 0 | ( | x | + | 5 | ) |
| 1 | + | 2 | ÷ | ( | x | + | 4 | ) | × | x | + | 2 | ÷ | ( | x | + | 4 | ) | × | 5 | - | 3 | ÷ | ( | x | + | 3 | ) | × | ( | x | + | 5 | ) | - | 3 | ÷ | ( | x | + | 2 | ) | × | ( | x | + | 5 | ) | + | 2 | ÷ | ( | x | + | 1 | ) | × | ( | x | + | 5 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | = | 0 | x | + | 0 | × | 5 |
| 1 | + | 2 | ÷ | ( | x | + | 4 | ) | × | x | + | 10 | ÷ | ( | x | + | 4 | ) | - | 3 | ÷ | ( | x | + | 3 | ) | × | ( | x | + | 5 | ) | - | 3 | ÷ | ( | x | + | 2 | ) | × | ( | x | + | 5 | ) | + | 2 | ÷ | ( | x | + | 1 | ) | × | ( | x | + | 5 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | = | 0 | x | + | 0 |
| 方程两边同时乘以： | ( | x | + | 4 | ) |
| 1 | ( | x | + | 4 | ) | + | 2 | x | + | 10 | - | 3 | ÷ | ( | x | + | 3 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | - | 3 | ÷ | ( | x | + | 2 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | + | 2 | ÷ | ( | x | + | 1 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | = | 0 | x | ( | x | + | 4 | ) | + | 0 | ( | x | + | 4 | ) |
| 1 | x | + | 1 | × | 4 | + | 2 | x | + | 10 | - | 3 | ÷ | ( | x | + | 3 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | - | 3 | ÷ | ( | x | + | 2 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | + | 2 | ÷ | ( | x | + | 1 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | = | 0 | x | ( | x | + | 4 | ) | + | 0 | ( | x | + | 4 | ) |
| 1 | x | + | 1 | × | 4 | + | 2 | x | + | 10 | - | 3 | ÷ | ( | x | + | 3 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | - | 3 | ÷ | ( | x | + | 2 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | + | 2 | ÷ | ( | x | + | 1 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | = | 0 | x | x | + | 0 | x | × | 4 | + | 0 | ( | x | + | 4 | ) |
| 1 | x | + | 4 | + | 2 | x | + | 10 | - | 3 | ÷ | ( | x | + | 3 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | - | 3 | ÷ | ( | x | + | 2 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | + | 2 | ÷ | ( | x | + | 1 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | = | 0 | x | x | + | 0 | x | + | 0 | ( | x | + | 4 | ) |
| 3 | x | + | 14 | - | 3 | ÷ | ( | x | + | 3 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | - | 3 | ÷ | ( | x | + | 2 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | + | 2 | ÷ | ( | x | + | 1 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | = | 0 | x | x | + | 0 | x | + | 0 | ( | x | + | 4 | ) |
| 方程两边同时乘以： | ( | x | + | 3 | ) |
| 3 | x | ( | x | + | 3 | ) | + | 14 | ( | x | + | 3 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | - | 3 | ÷ | ( | x | + | 2 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | + | 2 | ÷ | ( | x | + | 1 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | = | 0 | ( | x | + | 3 | ) |
| 3 | x | x | + | 3 | x | × | 3 | + | 14 | ( | x | + | 3 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | - | 3 | ÷ | ( | x | + | 2 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | + | 2 | ÷ | ( | x | + | 1 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | = | 0 | ( | x | + | 3 | ) |
| 3 | x | x | + | 3 | x | × | 3 | + | 14 | ( | x | + | 3 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | - | 3 | ÷ | ( | x | + | 2 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | + | 2 | ÷ | ( | x | + | 1 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | = | 0 | x | + | 0 | × | 3 |
| 3 | x | x | + | 9 | x | + | 14 | ( | x | + | 3 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | - | 3 | ÷ | ( | x | + | 2 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | + | 2 | ÷ | ( | x | + | 1 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | = | 0 | x | + | 0 |
| 方程两边同时乘以： | ( | x | + | 2 | ) |
| 3 | x | x | ( | x | + | 2 | ) | + | 9 | x | ( | x | + | 2 | ) | + | 14 | ( | x | + | 3 | ) | ( | x | + | 2 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 2 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | + | 2 | ÷ | ( | x | + | 1 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 2 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 2 | ) | = | 0 | ( | x | + | 2 | ) |
| 3 | x | x | x | + | 3 | x | x | × | 2 | + | 9 | x | ( | x | + | 2 | ) | + | 14 | ( | x | + | 3 | ) | ( | x | + | 2 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 2 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | + | 2 | ÷ | ( | x | + | 1 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 2 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 2 | ) | = | 0 | ( | x | + | 2 | ) |
| 3 | x | x | x | + | 3 | x | x | × | 2 | + | 9 | x | ( | x | + | 2 | ) | + | 14 | ( | x | + | 3 | ) | ( | x | + | 2 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 2 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | + | 2 | ÷ | ( | x | + | 1 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 2 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 2 | ) | = | 0 | x | + | 0 | × | 2 |
| 3 | x | x | x | + | 6 | x | x | + | 9 | x | ( | x | + | 2 | ) | + | 14 | ( | x | + | 3 | ) | ( | x | + | 2 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 2 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | + | 2 | ÷ | ( | x | + | 1 | ) | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 2 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 2 | ) | = | 0 | x | + | 0 |
| 方程两边同时乘以： | ( | x | + | 1 | ) |
| 3 | x | x | x | ( | x | + | 1 | ) | + | 6 | x | x | ( | x | + | 1 | ) | + | 9 | x | ( | x | + | 2 | ) | ( | x | + | 1 | ) | + | 14 | ( | x | + | 3 | ) | ( | x | + | 2 | ) | ( | x | + | 1 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 2 | ) | ( | x | + | 1 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 1 | ) | + | 2 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 2 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 2 | ) | ( | x | + | 1 | ) | = | 0 | ( | x | + | 1 | ) |
| 3 | x | x | x | x | + | 3 | x | x | x | × | 1 | + | 6 | x | x | ( | x | + | 1 | ) | + | 9 | x | ( | x | + | 2 | ) | ( | x | + | 1 | ) | + | 14 | ( | x | + | 3 | ) | ( | x | + | 2 | ) | ( | x | + | 1 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 2 | ) | ( | x | + | 1 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 1 | ) | + | 2 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 2 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 2 | ) | ( | x | + | 1 | ) | = | 0 | ( | x | + | 1 | ) |
| 3 | x | x | x | x | + | 3 | x | x | x | × | 1 | + | 6 | x | x | ( | x | + | 1 | ) | + | 9 | x | ( | x | + | 2 | ) | ( | x | + | 1 | ) | + | 14 | ( | x | + | 3 | ) | ( | x | + | 2 | ) | ( | x | + | 1 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 2 | ) | ( | x | + | 1 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 1 | ) | + | 2 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 2 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 2 | ) | ( | x | + | 1 | ) | = | 0 | x | + | 0 | × | 1 |
| 3 | x | x | x | x | + | 3 | x | x | x | + | 6 | x | x | ( | x | + | 1 | ) | + | 9 | x | ( | x | + | 2 | ) | ( | x | + | 1 | ) | + | 14 | ( | x | + | 3 | ) | ( | x | + | 2 | ) | ( | x | + | 1 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 2 | ) | ( | x | + | 1 | ) | - | 3 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 1 | ) | + | 2 | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 2 | ) | + | 1 | ÷ | x | × | ( | x | + | 5 | ) | ( | x | + | 4 | ) | ( | x | + | 3 | ) | ( | x | + | 2 | ) | ( | x | + | 1 | ) | = | 0 | x | + | 0 |
方程化为一般式后，有公因式：
( 2x + 5 )
由
2x + 5 = 0
得：
| x1= | - | 5 2 |
不能由因式分解法得出的解：
x2≈-4.462142 ，保留6位小数
x3≈-0.537858 ，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》