| 2 | ÷ | ( | x | + | 2 | ) | + | 1 | ÷ | ( | x | + | 5 | ) | = | 1 | ÷ | ( | x | − | 1 | ) |
| Multiply both sides of the equation by: | ( | x | + | 2 | ) | , | ( | x | − | 1 | ) |
| 2 | ( | x | − | 1 | ) | + | 1 | ÷ | ( | x | + | 5 | ) | × | ( | x | + | 2 | ) | ( | x | − | 1 | ) | = | 1 | ( | x | + | 2 | ) |
| 2 | x | − | 2 | × | 1 | + | 1 | ÷ | ( | x | + | 5 | ) | × | ( | x | + | 2 | ) | ( | x | − | 1 | ) | = | 1 | ( | x | + | 2 | ) |
| 2 | x | − | 2 | × | 1 | + | 1 | ÷ | ( | x | + | 5 | ) | × | ( | x | + | 2 | ) | ( | x | − | 1 | ) | = | 1 | x | + | 1 | × | 2 |
| 2 | x | − | 2 | + | 1 | ÷ | ( | x | + | 5 | ) | × | ( | x | + | 2 | ) | ( | x | − | 1 | ) | = | 1 | x | + | 2 |
| Multiply both sides of the equation by: | ( | x | + | 5 | ) |
| 2 | x | ( | x | + | 5 | ) | − | 2 | ( | x | + | 5 | ) | + | 1 | ( | x | + | 2 | ) | ( | x | − | 1 | ) | = | 1 | x | ( | x | + | 5 | ) | + | 2 | ( | x | + | 5 | ) |
| 2 | x | x | + | 2 | x | × | 5 | − | 2 | ( | x | + | 5 | ) | + | 1 | ( | x | + | 2 | ) | ( | x | − | 1 | ) | = | 1 | x | ( | x | + | 5 | ) | + | 2 | ( | x | + | 5 | ) |
| 2 | x | x | + | 2 | x | × | 5 | − | 2 | ( | x | + | 5 | ) | + | 1 | ( | x | + | 2 | ) | ( | x | − | 1 | ) | = | 1 | x | x | + | 1 | x | × | 5 | + | 2 | ( | x | + | 5 | ) |
| 2 | x | x | + | 10 | x | − | 2 | ( | x | + | 5 | ) | + | 1 | ( | x | + | 2 | ) | ( | x | − | 1 | ) | = | 1 | x | x | + | 5 | x | + | 2 | ( | x | + | 5 | ) |
| 2 | x | x | + | 10 | x | − | 2 | x | − | 2 | × | 5 | + | 1 | ( | x | + | 2 | ) | ( | x | − | 1 | ) | = | 1 | x | x | + | 5 | x | + | 2 | ( | x | + | 5 | ) |
| 2 | x | x | + | 10 | x | − | 2 | x | − | 2 | × | 5 | + | 1 | ( | x | + | 2 | ) | ( | x | − | 1 | ) | = | 1 | x | x | + | 5 | x | + | 2 | x | + | 2 | × | 5 |
| 2 | x | x | + | 10 | x | − | 2 | x | − | 10 | + | 1 | ( | x | + | 2 | ) | ( | x | − | 1 | ) | = | 1 | x | x | + | 5 | x | + | 2 | x | + | 10 |
| 2 | x | x | + | 8 | x | − | 10 | + | 1 | ( | x | + | 2 | ) | ( | x | − | 1 | ) | = | 1 | x | x | + | 7 | x | + | 10 |
| 2 | x | x | + | 8 | x | − | 10 | + | 1 | x | ( | x | − | 1 | ) | + | 1 | × | 2 | ( | x | − | 1 | ) | = | 1 | x | x | + | 7 | x | + | 10 |
| 2 | x | x | + | 8 | x | − | 10 | + | 1 | x | ( | x | − | 1 | ) | + | 2 | ( | x | − | 1 | ) | = | 1 | x | x | + | 7 | x | + | 10 |
| 2 | x | x | + | 8 | x | − | 10 | + | 1 | x | x | − | 1 | x | × | 1 | = | 1 | x | x | + | 7 | x | + | 10 |
| 2 | x | x | + | 8 | x | − | 10 | + | 1 | x | x | − | 1 | x | + | 2 | = | 1 | x | x | + | 7 | x | + | 10 |
| 2 | x | x | + | 7 | x | − | 10 | + | 1 | x | x | + | 2 | ( | x | − | 1 | ) | = | 1 | x | x | + | 7 | x | + | 10 |
| 2 | x | x | + | 7 | x | − | 10 | + | 1 | x | x | + | 2 | x | − | 2 | = | 1 | x | x | + | 7 | x | + | 10 |
| 2 | x | x | + | 7 | x | − | 10 | + | 1 | x | x | + | 2 | x | − | 2 | = | 1 | x | x | + | 7 | x | + | 10 |
| 2 | x | x | + | 9 | x | − | 12 | + | 1 | x | x | = | 1 | x | x | + | 7 | x | + | 10 |