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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 1/n+1/（n+1）+1/（n+2） = 107/210 .
    Question type: Equation
    Solution:Original question:
     1 ÷ n + 1 ÷ ( n + 1) + 1 ÷ ( n + 2) = 107 ÷ 210
     Multiply both sides of the equation by: n
     1 + 1 ÷ ( n + 1) × n + 1 ÷ ( n + 2) × n = 107 ÷ 210 × n
     Multiply both sides of the equation by:( n + 1)
     1( n + 1) + 1 n + 1 ÷ ( n + 2) × n ( n + 1) = 107 ÷ 210 × n ( n + 1)
    Remove a bracket on the left of the equation:
     1 n + 1 × 1 + 1 n + 1 ÷ ( n + 2) × n ( n + 1) = 107 ÷ 210 × n ( n + 1)
    Remove a bracket on the right of the equation:：
     1 n + 1 × 1 + 1 n + 1 ÷ ( n + 2) × n ( n + 1) = 107 ÷ 210 × n n + 107 ÷ 210 × n × 1
    The equation is reduced to :
     1 n + 1 + 1 n + 1 ÷ ( n + 2) × n ( n + 1) =
107
210
 n n +
107
210
 n
    The equation is reduced to :
     2 n + 1 + 1 ÷ ( n + 2) × n ( n + 1) =
107
210
 n n +
107
210
 n
     Multiply both sides of the equation by:( n + 2)
     2 n ( n + 2) + 1( n + 2) + 1 n ( n + 1) =
107
210
 n n ( n + 2) +
107
210
 n ( n + 2)
    Remove a bracket on the left of the equation:
     2 n n + 2 n × 2 + 1( n + 2) + 1 n ( n + 1) =
107
210
 n n ( n + 2) +
107
210
 n ( n + 2)
    Remove a bracket on the right of the equation:：
     2 n n + 2 n × 2 + 1( n + 2) + 1 n ( n + 1) =
107
210
 n n n +
107
210
 n n × 2 +
107
210
 n ( n + 2)
    The equation is reduced to :
     2 n n + 4 n + 1( n + 2) + 1 n ( n + 1) =
107
210
 n n n +
107
105
 n n +
107
210
 n ( n + 2)
    Remove a bracket on the left of the equation:
     2 n n + 4 n + 1 n + 1 × 2 + 1 n ( n + 1) =
107
210
 n n n +
107
105
 n n +
107
210
 n ( n + 2)
    Remove a bracket on the right of the equation:：
     2 n n + 4 n + 1 n + 1 × 2 + 1 n ( n + 1) =
107
210
 n n n +
107
105
 n n +
107
210
 n n +
107
210
 n
    The equation is reduced to :
     2 n n + 4 n + 1 n + 2 + 1 n ( n + 1) =
107
210
 n n n +
107
105
 n n +
107
210
 n n +
107
105
 n
    The equation is reduced to :
     2 n n + 5 n + 2 + 1 n ( n + 1) =
107
210
 n n n +
107
105
 n n +
107
210
 n n +
107
105
 n
    Remove a bracket on the left of the equation:
     2 n n + 5 n + 2 + 1 n n + 1 n × 1 =
107
210
 n n n +
107
105
 n n +
107
210
 n n +
107
105
 n
    The equation is reduced to :
     2 n n + 5 n + 2 + 1 n n + 1 n =
107
210
 n n n +
107
105
 n n +
107
210
 n n +
107
105
 n
    The equation is reduced to :
     2 n n + 6 n + 2 + 1 n n =
107
210
 n n n +
107
105
 n n +
107
210
 n n +
107
105
 n

    After the equation is converted into a general formula, there is a common factor:
    ( n - 5 )
    From
        n - 5 = 0
    it is concluded that:：
        n1=5

    Solutions that cannot be obtained by factorization:
        n2≈-1.630746 , keep 6 decimal places
        n3≈-0.481403 , keep 6 decimal places    
    There are 3 solution(s).

解程的详细方法请参阅：《方程的解法》


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