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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+2)/(x+1)+(x+8)/(x+7) = (x+6)/(x+5)+(x+4)x(x+3) .
    Question type: Equation
    Solution:Original question:
     ( x + 2) ÷ ( x + 1) + ( x + 8) ÷ ( x + 7) = ( x + 6) ÷ ( x + 5) + ( x + 4) x ( x + 3)
     Multiply both sides of the equation by:( x + 1) ,  ( x + 5)
     ( x + 2)( x + 5) + ( x + 8) ÷ ( x + 7) × ( x + 1)( x + 5) = ( x + 6)( x + 1) + ( x + 4) x ( x + 3)( x + 1)( x + 5)
    Remove a bracket on the left of the equation:：
      x ( x + 5) + 2( x + 5) + ( x + 8) ÷ ( x + 7) × ( x + 1)( x + 5) = ( x + 6)( x + 1) + ( x + 4) x ( x + 3)( x + 1)( x + 5)
    Remove a bracket on the right of the equation:：
      x ( x + 5) + 2( x + 5) + ( x + 8) ÷ ( x + 7) × ( x + 1)( x + 5) = x ( x + 1) + 6( x + 1) + ( x + 4) x ( x + 3)( x + 1)( x + 5)
     Multiply both sides of the equation by:( x + 7)
      x ( x + 5)( x + 7) + 2( x + 5)( x + 7) + ( x + 8)( x + 1)( x + 5) = x ( x + 1)( x + 7) + 6( x + 1)( x + 7) + ( x + 4) x ( x + 3)( x + 1)( x + 5)( x + 7)
    Remove a bracket on the left of the equation:
      x x ( x + 7) + x × 5( x + 7) + 2( x + 5)( x + 7) + ( x + 8)( x + 1)( x + 5) = x ( x + 1)( x + 7) + 6( x + 1)( x + 7) + ( x + 4) x ( x + 3)( x + 1)( x + 5)( x + 7)
    Remove a bracket on the right of the equation:：
      x x ( x + 7) + x × 5( x + 7) + 2( x + 5)( x + 7) + ( x + 8)( x + 1)( x + 5) = x x ( x + 7) + x × 1( x + 7) + 6( x + 1)( x + 7) + ( x + 4) x ( x + 3)
    Remove a bracket on the left of the equation:
      x x x + x x × 7 + x × 5( x + 7) + 2( x + 5)( x + 7) = x x ( x + 7) + x × 1( x + 7) + 6( x + 1)( x + 7) + ( x + 4) x ( x + 3)
    Remove a bracket on the right of the equation:：
      x x x + x x × 7 + x × 5( x + 7) + 2( x + 5)( x + 7) = x x x + x x × 7 + x × 1( x + 7) + 6( x + 1)( x + 7)
    Remove a bracket on the left of the equation:
      x x x + x x × 7 + x × 5 x + x × 5 × 7 = x x x + x x × 7 + x × 1( x + 7) + 6( x + 1)( x + 7)
    Remove a bracket on the right of the equation:：
      x x x + x x × 7 + x × 5 x + x × 5 × 7 = x x x + x x × 7 + x × 1 x + x × 1 × 7
    The equation is reduced to :
      x x x + x x × 7 + x × 5 x + x × 35 + 2 = x x x + x x × 7 + x × 1 x + x × 7 + 6
    Remove a bracket on the left of the equation:
      x x x + x x × 7 + x × 5 x + 35 x + 2 = x x x + x x × 7 + x × 1 x + 7 x + 6
    Remove a bracket on the right of the equation:：
      x x x + x x × 7 + x × 5 x + 35 x + 2 = x x x + x x × 7 + x × 1 x + 7 x + 6
    The equation is reduced to :
      x x x + x x × 7 + x × 5 x + 35 x + 2 = x x x + x x × 7 + x × 1 x + 7 x + 6
    Remove a bracket on the left of the equation:
      x x x + x x × 7 + x × 5 x + 35 x + 2 = x x x + x x × 7 + x × 1 x + 7 x + 6
    Remove a bracket on the right of the equation:：
      x x x + x x × 7 + x × 5 x + 35 x + 2 = x x x + x x × 7 + x × 1 x + 7 x + 6
    The equation is reduced to :
      x x x + x x × 7 + x × 5 x + 35 x + 2 = x x x + x x × 7 + x × 1 x + 7 x + 6
    The equation is reduced to :
      x x x + x x × 7 + x × 5 x + 49 x + 2 = x x x + x x × 7 + x × 1 x + 49 x + 6
    Remove a bracket on the left of the equation:
      x x x + x x × 7 + x × 5 x + 49 x + 2 = x x x + x x × 7 + x × 1 x + 49 x + 6
    Remove a bracket on the right of the equation:：
      x x x + x x × 7 + x × 5 x + 49 x + 2 = x x x + x x × 7 + x × 1 x + 49 x + 6
    The equation is reduced to :
      x x x + x x × 7 + x × 5 x + 49 x + 2 = x x x + x x × 7 + x × 1 x + 49 x + 6
    The equation is reduced to :
      x x x + x x × 7 + x × 5 x + 59 x + 2 = x x x + x x × 7 + x × 1 x + 55 x + 6

    After the equation is converted into a general formula, there is a common factor:
    ( x + 4 )
    From
        x + 4 = 0
    it is concluded that:：
        x1=-4

    Solutions that cannot be obtained by factorization:
        x2≈-4.894954 , keep 6 decimal places
        x3≈-3.090252 , keep 6 decimal places
        x4≈-1.143358 , keep 6 decimal places
        x5≈0.140186 , keep 6 decimal places    
    There are 5 solution(s).

解程的详细方法请参阅：《方程的解法》



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