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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.
    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 x+1÷(1-x)+(x-1)÷x = 19÷6 .
    Question type: Equation
    Solution:Original question:
      x + 1 ÷ (1 x ) + ( x 1) ÷ x = 19 ÷ 6
     Multiply both sides of the equation by:(1 x )
      x (1 x ) + 1 + ( x 1) ÷ x × (1 x ) = 19 ÷ 6 × (1 x )
    Remove a bracket on the left of the equation::
      x × 1 x x + 1 + ( x 1) ÷ x × (1 x ) = 19 ÷ 6 × (1 x )
    Remove a bracket on the right of the equation::
      x × 1 x x + 1 + ( x 1) ÷ x × (1 x ) = 19 ÷ 6 × 119 ÷ 6 × x
    The equation is reduced to :
      x × 1 x x + 1 + ( x 1) ÷ x × (1 x ) =
19
6
19
6
x
     Multiply both sides of the equation by: x
     1 x x x x x + 1 x + ( x 1)(1 x ) =
19
6
x
19
6
x x
    Remove a bracket on the left of the equation:
     1 x x x x x + 1 x + x (1 x )1(1 x ) =
19
6
x
19
6
x x
    Remove a bracket on the left of the equation:
     1 x x x x x + 1 x + x × 1 x x =
19
6
x
19
6
x x
    The equation is reduced to :
     1 x x x x x + 2 x x x 1(1 x ) =
19
6
x
19
6
x x
    Remove a bracket on the left of the equation:
     1 x x x x x + 2 x x x 1 × 1 =
19
6
x
19
6
x x
    The equation is reduced to :
     1 x x x x x + 2 x x x 1 + 1 =
19
6
x
19
6
x x
    The equation is reduced to :
     1 x x x x x + 3 x x x 1 =
19
6
x
19
6
x x

    After the equation is converted into a general formula, it is converted into:
    ( 2x + 1 )( 3x - 2 )( x - 3 )=0
    From
        2x + 1 = 0
        3x - 2 = 0
        x - 3 = 0

    it is concluded that::
        x1=-
1
2
        x2=
2
3
        x3=3
    
    There are 3 solution(s).


解程的详细方法请参阅:《方程的解法》



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