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Work: Find the solution of equation ((100+x)(300-2x))/(100(200-x)) = 0 .
Question type: Equation
Solution:Original question:| | ( | ( | 100 | + | x | ) | ( | 300 | − | 2 | x | ) | ) | ÷ | ( | 100 | ( | 200 | − | x | ) | ) | = | 0 |
| Multiply both sides of the equation by: | ( | 100 | ( | 200 | − | x | ) | ) |
| | ( | ( | 100 | + | x | ) | ( | 300 | − | 2 | x | ) | ) | = | 0 |
Remove a bracket on the left of the equation:：
| | ( | 100 | + | x | ) | ( | 300 | − | 2 | x | ) | = | 0 |
Remove a bracket on the left of the equation:
| | 100 | ( | 300 | − | 2 | x | ) | + | x | ( | 300 | − | 2 | x | ) | = | 0 |
Remove a bracket on the left of the equation:
| | 100 | × | 300 | − | 100 | × | 2 | x | + | x | ( | 300 | − | 2 | x | ) | = | 0 |
The equation is reduced to :
| | 30000 | − | 200 | x | + | x | ( | 300 | − | 2 | x | ) | = | 0 |
Remove a bracket on the left of the equation:
| | 30000 | − | 200 | x | + | x | × | 300 | − | x | × | 2 | x | = | 0 |
The equation is reduced to :
| | 30000 | + | 100 | x | − | x | × | 2 | x | = | 0 |
After the equation is converted into a general formula, it is converted into:
( x + 100 )( x - 150 )=0
From
x + 100 = 0
x - 150 = 0
it is concluded that:：
x1=-100
x2=150
There are 2 solution(s).
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