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           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation 11315496/(670+0.2x)+7543664/(670+x)+25931010/(670+0.1x)+17287340/(670+x) = 9092034÷(670+0.1x)+6061356/(670+x)+32734.8+14621554/(670+x) .
    Question type: Equation
    Solution:Original question:
     11315496 ÷ (670 +
1
5
x ) + 7543664 ÷ (670 + x ) + 25931010 ÷ (670 +
1
10
x ) + 17287340 ÷ (670 + x ) = 9092034 ÷ (670 +
1
10
x ) + 6061356 ÷ (670 + x ) +
163674
5
+ 14621554 ÷ (670 + x )
     Multiply both sides of the equation by:(670 +
1
5
x ) ,  (670 +
1
10
x )
     11315496(670 +
1
10
x ) + 7543664 ÷ (670 + x ) × (670 +
1
5
x )(670 +
1
10
x ) + 25931010(670 +
1
5
x ) + 17287340 ÷ (670 + x ) × (670 +
1
5
x )(670 +
1
10
x ) = 9092034(670 +
1
5
x ) + 6061356 ÷ (670 + x ) × (670 +
1
5
x )(670 +
1
10
x ) +
163674
5
(670 +
1
5
x )(670 +
1
10
x ) + 14621554 ÷ (670 + x ) × (670 +
1
5
x )
    Remove a bracket on the left of the equation::
     11315496 × 670 + 11315496 ×
1
10
x + 7543664 ÷ (670 + x ) × (670 +
1
5
x )(670 +
1
10
x ) + 25931010(670 +
1
5
x ) + 17287340 = 9092034(670 +
1
5
x ) + 6061356 ÷ (670 + x ) × (670 +
1
5
x )(670 +
1
10
x ) +
163674
5
(670 +
1
5
x )(670 +
1
10
x ) + 14621554 ÷ (670 + x ) × (670 +
1
5
x )
    Remove a bracket on the right of the equation::
     11315496 × 670 + 11315496 ×
1
10
x + 7543664 ÷ (670 + x ) × (670 +
1
5
x )(670 +
1
10
x ) + 25931010(670 +
1
5
x ) + 17287340 = 9092034 × 670 + 9092034 ×
1
5
x + 6061356 ÷ (670 + x ) × (670 +
1
5
x )(670 +
1
10
x ) +
163674
5
(670 +
1
5
x )(670 +
1
10
x )
    The equation is reduced to :
     7581382320 +
5657748
5
x + 7543664 ÷ (670 + x ) × (670 +
1
5
x )(670 +
1
10
x ) + 25931010(670 +
1
5
x ) + 17287340 ÷ (670 + x ) × (670 +
1
5
x ) = 6091662780 +
9092034
5
x + 6061356 ÷ (670 + x ) × (670 +
1
5
x )(670 +
1
10
x ) +
163674
5
(670 +
1
5
x )(670 +
1
10
x ) + 14621554 ÷ (670 + x )
     Multiply both sides of the equation by:(670 + x )
     7581382320(670 + x ) +
5657748
5
x (670 + x ) + 7543664(670 +
1
5
x )(670 +
1
10
x ) + 25931010(670 +
1
5
x )(670 + x ) + 17287340 = 6091662780(670 + x ) +
9092034
5
x (670 + x ) + 6061356(670 +
1
5
x )(670 +
1
10
x ) +
163674
5
(670 +
1
5
x )(670 +
1
10
x )(670 + x )
    Remove a bracket on the left of the equation:
     7581382320 × 670 + 7581382320 x +
5657748
5
x (670 + x ) + 7543664(670 +
1
5
x )(670 +
1
10
x ) + 25931010(670 +
1
5
x ) = 6091662780(670 + x ) +
9092034
5
x (670 + x ) + 6061356(670 +
1
5
x )(670 +
1
10
x ) +
163674
5
(670 +
1
5
x )(670 +
1
10
x )(670 + x )
    Remove a bracket on the right of the equation::
     7581382320 × 670 + 7581382320 x +
5657748
5
x (670 + x ) + 7543664(670 +
1
5
x )(670 +
1
10
x ) + 25931010(670 +
1
5
x ) = 6091662780 × 670 + 6091662780 x +
9092034
5
x (670 + x ) + 6061356(670 +
1
5
x )(670 +
1
10
x ) +
163674
5
(670 +
1
5
x )
    
    There are 0 solution(s).


解程的详细方法请参阅:《方程的解法》



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