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[ 1/1 Equation]
Work: Find the solution of equation (-4t/5+6)（8-8t/5)/(-t+19/2) = 0 .
Question type: Equation
Solution:Original question:| | ( | - | 4 | t | ÷ | 5 | + | 6 | ) | ( | 8 | − | 8 | t | ÷ | 5 | ) | ÷ | ( | - | t | + | 19 | ÷ | 2 | ) | = | 0 |
| Multiply both sides of the equation by: | ( | - | t | + | 19 | ÷ | 2 | ) |
| | ( | - | 4 | t | ÷ | 5 | + | 6 | ) | ( | 8 | − | 8 | t | ÷ | 5 | ) | = | 0 |
Remove a bracket on the left of the equation:：
| | - | 4 | t | ÷ | 5 | × | ( | 8 | − | 8 | t | ÷ | 5 | ) | + | 6 | ( | 8 | − | 8 | t | ÷ | 5 | ) | = | 0 |
The equation is reduced to :
| | - | 4 5 | t | ( | 8 | − | 8 | t | ÷ | 5 | ) | + | 6 | ( | 8 | − | 8 | t | ÷ | 5 | ) | = | 0 |
Remove a bracket on the left of the equation:
| | - | 4 5 | t | × | 8 | + | 4 5 | t | × | 8 | t | ÷ | 5 | + | 6 | ( | 8 | − | 8 | t | ÷ | 5 | ) | = | 0 |
The equation is reduced to :
| | - | 32 5 | t | + | 32 25 | t | t | + | 6 | ( | 8 | − | 8 | t | ÷ | 5 | ) | = | 0 |
Remove a bracket on the left of the equation:
| | - | 32 5 | t | + | 32 25 | t | t | + | 6 | × | 8 | − | 6 | × | 8 | t | ÷ | 5 | = | 0 |
The equation is reduced to :
| | - | 32 5 | t | + | 32 25 | t | t | + | 48 | − | 48 5 | t | = | 0 |
The equation is reduced to :
| | - | 16 | t | + | 32 25 | t | t | + | 48 | = | 0 |
After the equation is converted into a general formula, it is converted into:
( t - 5 )( 2t - 15 )=0
From
t - 5 = 0
2t - 15 = 0
it is concluded that:：
t1=5
There are 2 solution(s).
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