| k | − | ( | 5 | ÷ | 13 | − | k | ) | ( | 5 | ÷ | 13 | − | k | ) | = | 0 |
| 方程左边 = | k | − | 5 | ÷ | 13 | × | ( | 5 | ÷ | 13 | − | k | ) | + | k | ( | 5 | ÷ | 13 | − | k | ) |
| = | k | − | 5 13 | ( | 5 | ÷ | 13 | − | k | ) | + | k | ( | 5 | ÷ | 13 | − | k | ) |
| = | k | − | 5 13 | × | 5 | ÷ | 13 | + | 5 13 | k | + | k | ( | 5 | ÷ | 13 | − | k | ) |
| = | k | − | 25 169 | + | 5 13 | k | + | k | ( | 5 | ÷ | 13 | − | k | ) |
| = | 18 13 | k | − | 25 169 | + | k | ( | 5 | ÷ | 13 | − | k | ) |
| = | 18 13 | k | − | 25 169 | + | k | × | 5 | ÷ | 13 | − | k | k |
| = | 18 13 | k | − | 25 169 | + | k | × | 5 13 | − | k | k |
| = | 23 13 | k | − | 25 169 | − | k | k |
23 13 | k | − | 25 169 | − | k | k | = | 0 |