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[ 1/1 Equation]
Work: Find the solution of equation 1/d+1/(d+25)+1/(d+100) = 1/(d+38) .
Question type: Equation
Solution:Original question:| | 1 | ÷ | d | + | 1 | ÷ | ( | d | + | 25 | ) | + | 1 | ÷ | ( | d | + | 100 | ) | = | 1 | ÷ | ( | d | + | 38 | ) |
| Multiply both sides of the equation by: | d | , | ( | d | + | 38 | ) |
| | 1 | ( | d | + | 38 | ) | + | 1 | ÷ | ( | d | + | 25 | ) | × | d | ( | d | + | 38 | ) | + | 1 | ÷ | ( | d | + | 100 | ) | × | d | ( | d | + | 38 | ) | = | 1 | d |
Remove a bracket on the left of the equation:：
| | 1 | d | + | 1 | × | 38 | + | 1 | ÷ | ( | d | + | 25 | ) | × | d | ( | d | + | 38 | ) | + | 1 | ÷ | ( | d | + | 100 | ) | × | d | ( | d | + | 38 | ) | = | 1 | d |
The equation is reduced to :
| | 1 | d | + | 38 | + | 1 | ÷ | ( | d | + | 25 | ) | × | d | ( | d | + | 38 | ) | + | 1 | ÷ | ( | d | + | 100 | ) | × | d | ( | d | + | 38 | ) | = | 1 | d |
| Multiply both sides of the equation by: | ( | d | + | 25 | ) |
| | 1 | d | ( | d | + | 25 | ) | + | 38 | ( | d | + | 25 | ) | + | 1 | d | ( | d | + | 38 | ) | + | 1 | ÷ | ( | d | + | 100 | ) | × | d | ( | d | + | 38 | ) | = | 1 | d | ( | d | + | 25 | ) |
Remove a bracket on the left of the equation:
| | 1 | d | d | + | 1 | d | × | 25 | + | 38 | ( | d | + | 25 | ) | + | 1 | d | ( | d | + | 38 | ) | + | 1 | = | 1 | d | ( | d | + | 25 | ) |
Remove a bracket on the right of the equation:：
| | 1 | d | d | + | 1 | d | × | 25 | + | 38 | ( | d | + | 25 | ) | + | 1 | d | ( | d | + | 38 | ) | + | 1 | = | 1 | d | d | + | 1 | d | × | 25 |
The equation is reduced to :
| | 1 | d | d | + | 25 | d | + | 38 | ( | d | + | 25 | ) | + | 1 | d | ( | d | + | 38 | ) | + | 1 | ÷ | ( | d | + | 100 | ) | = | 1 | d | d | + | 25 | d |
| Multiply both sides of the equation by: | ( | d | + | 100 | ) |
| | 1 | d | d | ( | d | + | 100 | ) | + | 25 | d | ( | d | + | 100 | ) | + | 38 | ( | d | + | 25 | ) | ( | d | + | 100 | ) | + | 1 | d | = | 1 | d | d | ( | d | + | 100 | ) | + | 25 | d | ( | d | + | 100 | ) |
Remove a bracket on the left of the equation:
| | 1 | d | d | d | + | 1 | d | d | × | 100 | + | 25 | d | ( | d | + | 100 | ) | + | 38 | = | 1 | d | d | ( | d | + | 100 | ) | + | 25 | d | ( | d | + | 100 | ) |
Remove a bracket on the right of the equation:：
| | 1 | d | d | d | + | 1 | d | d | × | 100 | + | 25 | d | ( | d | + | 100 | ) | + | 38 | = | 1 | d | d | d | + | 1 | d | d | × | 100 | + | 25 | d | ( | d | + | 100 | ) |
The equation is reduced to :
| | 1 | d | d | d | + | 100 | d | d | + | 25 | d | ( | d | + | 100 | ) | + | 38 | ( | d | + | 25 | ) | = | 1 | d | d | d | + | 100 | d | d | + | 25 | d | ( | d | + | 100 | ) |
Remove a bracket on the left of the equation:
| | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 25 | d | = | 1 | d | d | d | + | 100 | d | d | + | 25 | d | ( | d | + | 100 | ) |
Remove a bracket on the right of the equation:：
| | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 25 | d | = | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 25 | d |
The equation is reduced to :
| | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 2500 | d | = | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 2500 | d |
Remove a bracket on the left of the equation:
| | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 2500 | d | = | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 2500 | d |
The equation is reduced to :
| | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 2500 | d | = | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 2500 | d |
Remove a bracket on the left of the equation:
| | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 2500 | d | = | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 2500 | d |
The equation is reduced to :
| | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 2500 | d | = | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 2500 | d |
The equation is reduced to :
| | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 6300 | d | = | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 2500 | d |
Remove a bracket on the left of the equation:
| | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 6300 | d | = | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 2500 | d |
The equation is reduced to :
| | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 6300 | d | = | 1 | d | d | d | + | 100 | d | d | + | 25 | d | d | + | 2500 | d |
d≈-14.871593 , keep 6 decimal places
There are 1 solution(s).
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