| ( | x | − | 1 | ) | ÷ | ( | x | + | 1 | ) | = | ( | x | + | 2 | ) | ÷ | ( | x | + | 2 | ) |
| Multiply both sides of the equation by: | ( | x | + | 1 | ) | , | ( | x | + | 2 | ) |
| ( | x | − | 1 | ) | ( | x | + | 2 | ) | = | ( | x | + | 2 | ) | ( | x | + | 1 | ) |
| x | ( | x | + | 2 | ) | − | 1 | ( | x | + | 2 | ) | = | ( | x | + | 2 | ) | ( | x | + | 1 | ) |
| x | ( | x | + | 2 | ) | − | 1 | ( | x | + | 2 | ) | = | x | ( | x | + | 1 | ) | + | 2 | ( | x | + | 1 | ) |
| x | x | + | x | × | 2 | − | 1 | ( | x | + | 2 | ) | = | x | ( | x | + | 1 | ) | + | 2 | ( | x | + | 1 | ) |
| x | x | + | x | × | 2 | − | 1 | ( | x | + | 2 | ) | = | x | x | + | x | × | 1 | + | 2 | ( | x | + | 1 | ) |
| x | x | + | 2 | x | − | 1 | x | − | 1 | × | 2 | = | x | x | + | 1 | x | + | 2 | ( | x | + | 1 | ) |
| x | x | + | 2 | x | − | 1 | x | − | 1 | × | 2 | = | x | x | + | 1 | x | + | 2 | x | + | 2 | × | 1 |
| x | x | + | 2 | x | − | 1 | x | − | 2 | = | x | x | + | 1 | x | + | 2 | x | + | 2 |
| x | x | + | 1 | x | − | 2 | = | x | x | + | 3 | x | + | 2 |