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On line Solution of Monovariate Equation：
Input any unary equation directly, and then click the "Next" button to obtain the solution of the equation.
It supports equations that contain mathematical functions.
Input any unary equation directly, and then click the "Next" button to obtain the solution of the equation.
It supports equations that contain mathematical functions.
Current location：Equations > Monovariate Equation > The history of univariate equation calculation > Answer
Overview: 1 questions will be solved this time.Among them
☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation ((2*((1-3*x)/(x-2)))+1)/(3+((1-3*x)/(x-2))) = x .
Question type: Equation
Solution:Original question:
Remove a bracket on the left of the equation:：
Remove a bracket on the right of the equation:：
Remove a bracket on the left of the equation:
Remove a bracket on the right of the equation:：
Remove a bracket on the left of the equation:
Remove a bracket on the right of the equation:：
The equation is reduced to :
Remove a bracket on the left of the equation:
Remove a bracket on the right of the equation:：
The equation is reduced to :
Remove a bracket on the left of the equation:
Remove a bracket on the right of the equation:：
The equation is reduced to :
Remove a bracket on the left of the equation:
Remove a bracket on the right of the equation:：
The equation is reduced to :
The equation is reduced to :
Remove a bracket on the left of the equation:
Remove a bracket on the right of the equation:：
After the equation is converted into a general formula, it is converted into:
( 250000x + 194879 )( 1000000x + 645621 )( 20000x + 10883 )( 1000000x + 348581 )( 1000000x - 90741 )( 1000000x - 90741 )( 500000x - 125247 )( 500000x - 125247 )=0
From
250000x + 194879 = 0
1000000x + 645621 = 0
20000x + 10883 = 0
1000000x + 348581 = 0
1000000x - 90741 = 0
1000000x - 90741 = 0
500000x - 125247 = 0
500000x - 125247 = 0
it is concluded that:：
There are 8 solution(s).
解程的详细方法请参阅：《方程的解法》
☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation ((2*((1-3*x)/(x-2)))+1)/(3+((1-3*x)/(x-2))) = x .
Question type: Equation
Solution:Original question:
| ( | ( | 2 | ( | ( | 1 | − | 3 | x | ) | ÷ | ( | x | − | 2 | ) | ) | ) | + | 1 | ) | ÷ | ( | 3 | + | ( | ( | 1 | − | 3 | x | ) | ÷ | ( | x | − | 2 | ) | ) | ) | = | x |
| Multiply both sides of the equation by: | ( | 3 | + | ( | ( | 1 | − | 3 | x | ) | ÷ | ( | x | − | 2 | ) | ) | ) |
| ( | ( | 2 | ( | ( | 1 | − | 3 | x | ) | ÷ | ( | x | − | 2 | ) | ) | ) | + | 1 | ) | = | x | ( | 3 | + | ( | ( | 1 | − | 3 | x | ) | ÷ | ( | x | − | 2 | ) | ) | ) |
| ( | 2 | ( | ( | 1 | − | 3 | x | ) | ÷ | ( | x | − | 2 | ) | ) | ) | + | 1 | = | x | ( | 3 | + | ( | ( | 1 | − | 3 | x | ) | ÷ | ( | x | − | 2 | ) | ) | ) |
| ( | 2 | ( | ( | 1 | − | 3 | x | ) | ÷ | ( | x | − | 2 | ) | ) | ) | + | 1 | = | x | × | 3 | + | x | ( | ( | 1 | − | 3 | x | ) | ÷ | ( | x | − | 2 | ) | ) |
| 2 | ( | ( | 1 | − | 3 | x | ) | ÷ | ( | x | − | 2 | ) | ) | + | 1 | = | 3 | x | + | x | ( | ( | 1 | − | 3 | x | ) | ÷ | ( | x | − | 2 | ) | ) |
| 2 | ( | ( | 1 | − | 3 | x | ) | ÷ | ( | x | − | 2 | ) | ) | + | 1 | = | 3 | x | + | x | ( | 1 | − | 3 | x | ) | ÷ | ( | x | − | 2 | ) |
| Multiply both sides of the equation by: | ( | x | − | 2 | ) |
| 2 | ( | ( | 1 | − | 3 | x | ) | ÷ | ( | x | − | 2 | ) | ) | ( | x | − | 2 | ) | + | 1 | ( | x | − | 2 | ) | = | 3 | x | ( | x | − | 2 | ) | + | x | ( | 1 | − | 3 | x | ) |
| 2 | ( | 1 | − | 3 | x | ) | ÷ | ( | x | − | 2 | ) | × | ( | x | − | 2 | ) | + | 1 | ( | x | − | 2 | ) | = | 3 | x | ( | x | − | 2 | ) | + | x | ( | 1 | − | 3 | x | ) |
| 2 | ( | 1 | − | 3 | x | ) | ÷ | ( | x | − | 2 | ) | × | ( | x | − | 2 | ) | + | 1 | ( | x | − | 2 | ) | = | 3 | x | x | − | 3 | x | × | 2 | + | x | ( | 1 | − | 3 | x | ) |
| 2 | ( | 1 | − | 3 | x | ) | ÷ | ( | x | − | 2 | ) | × | ( | x | − | 2 | ) | + | 1 | ( | x | − | 2 | ) | = | 3 | x | x | − | 6 | x | + | x | ( | 1 | − | 3 | x | ) |
| Multiply both sides of the equation by: | ( | x | − | 2 | ) |
| 2 | ( | 1 | − | 3 | x | ) | ( | x | − | 2 | ) | + | 1 | ( | x | − | 2 | ) | ( | x | − | 2 | ) | = | 3 | x | x | ( | x | − | 2 | ) | − | 6 | x | ( | x | − | 2 | ) | + | x | ( | 1 | − | 3 | x | ) | ( | x | − | 2 | ) |
| 2 | × | 1 | ( | x | − | 2 | ) | − | 2 | × | 3 | x | ( | x | − | 2 | ) | + | 1 | ( | x | − | 2 | ) | ( | x | − | 2 | ) | = | 3 | x | x | ( | x | − | 2 | ) | − | 6 | x | ( | x | − | 2 | ) | + | x | ( | 1 | − | 3 | x | ) | ( | x | − | 2 | ) |
| 2 | × | 1 | ( | x | − | 2 | ) | − | 2 | × | 3 | x | ( | x | − | 2 | ) | + | 1 | ( | x | − | 2 | ) | ( | x | − | 2 | ) | = | 3 | x | x | x | − | 3 | x | x | × | 2 | − | 6 | x | ( | x | − | 2 | ) | + | x |
| 2 | ( | x | − | 2 | ) | − | 6 | x | ( | x | − | 2 | ) | + | 1 | ( | x | − | 2 | ) | ( | x | − | 2 | ) | = | 3 | x | x | x | − | 6 | x | x | − | 6 | x | ( | x | − | 2 | ) | + | x | ( | 1 | − | 3 | x | ) |
| 2 | x | − | 2 | × | 2 | − | 6 | x | ( | x | − | 2 | ) | + | 1 | ( | x | − | 2 | ) | ( | x | − | 2 | ) | = | 3 | x | x | x | − | 6 | x | x | − | 6 | x | ( | x | − | 2 | ) | + | x | ( | 1 | − | 3 | x | ) |
| 2 | x | − | 2 | × | 2 | − | 6 | x | ( | x | − | 2 | ) | + | 1 | ( | x | − | 2 | ) | ( | x | − | 2 | ) | = | 3 | x | x | x | − | 6 | x | x | − | 6 | x | x | + | 6 | x |
| 2 | x | − | 4 | − | 6 | x | ( | x | − | 2 | ) | + | 1 | ( | x | − | 2 | ) | ( | x | − | 2 | ) | = | 3 | x | x | x | − | 6 | x | x | − | 6 | x | x | + | 12 | x |
| 2 | x | − | 4 | − | 6 | x | x | + | 6 | x | × | 2 | + | 1 | ( | x | − | 2 | ) | ( | x | − | 2 | ) | = | 3 | x | x | x | − | 6 | x | x | − | 6 | x | x | + | 12 | x |
| 2 | x | − | 4 | − | 6 | x | x | + | 6 | x | × | 2 | + | 1 | ( | x | − | 2 | ) | ( | x | − | 2 | ) | = | 3 | x | x | x | − | 6 | x | x | − | 6 | x | x | + | 12 | x |
| 2 | x | − | 4 | − | 6 | x | x | + | 12 | x | + | 1 | ( | x | − | 2 | ) | ( | x | − | 2 | ) | = | 3 | x | x | x | − | 6 | x | x | − | 6 | x | x | + | 12 | x |
| 14 | x | − | 4 | − | 6 | x | x | + | 1 | ( | x | − | 2 | ) | ( | x | − | 2 | ) | = | 3 | x | x | x | − | 6 | x | x | − | 6 | x | x | + | 12 | x |
| 14 | x | − | 4 | − | 6 | x | x | + | 1 | x | ( | x | − | 2 | ) | − | 1 | × | 2 | ( | x | − | 2 | ) | = | 3 | x | x | x | − | 6 | x | x | − | 6 | x | x | + | 12 | x |
| 14 | x | − | 4 | − | 6 | x | x | + | 1 | x | ( | x | − | 2 | ) | − | 1 | × | 2 | ( | x | − | 2 | ) | = | 3 | x | x | x | − | 6 | x | x | − | 6 | x | x | + | 12 | x |
After the equation is converted into a general formula, it is converted into:
( 250000x + 194879 )( 1000000x + 645621 )( 20000x + 10883 )( 1000000x + 348581 )( 1000000x - 90741 )( 1000000x - 90741 )( 500000x - 125247 )( 500000x - 125247 )=0
From
250000x + 194879 = 0
1000000x + 645621 = 0
20000x + 10883 = 0
1000000x + 348581 = 0
1000000x - 90741 = 0
1000000x - 90741 = 0
500000x - 125247 = 0
500000x - 125247 = 0
it is concluded that:：
| x1= | - | 194879 250000 |
| x2= | - | 645621 1000000 |
| x3= | - | 10883 20000 |
| x4= | - | 348581 1000000 |
| x5= | 90741 1000000 |
| x6= | 90741 1000000 |
| x7= | 125247 500000 |
| x8= | 125247 500000 |
There are 8 solution(s).
解程的详细方法请参阅：《方程的解法》