| ( | 1 | − | 10 | x | ) | = | 1 | ÷ | ( | 1 | + | x | ) | × | 10 |
| Multiply both sides of the equation by: | ( | 1 | + | x | ) |
| ( | 1 | − | 10 | x | ) | ( | 1 | + | x | ) | = | 1 | × | 10 |
| 1 | ( | 1 | + | x | ) | − | 10 | x | ( | 1 | + | x | ) | = | 1 | × | 10 |
| 1 | ( | 1 | + | x | ) | − | 10 | x | ( | 1 | + | x | ) | = | 10 |
| 1 | × | 1 | + | 1 | x | − | 10 | x | ( | 1 | + | x | ) | = | 10 |
| 1 | + | 1 | x | − | 10 | x | ( | 1 | + | x | ) | = | 10 |
| 1 | + | 1 | x | − | 10 | x | × | 1 | − | 10 | x | x | = | 10 |
| 1 | + | 1 | x | − | 10 | x | − | 10 | x | x | = | 10 |
| 1 | − | 9 | x | − | 10 | x | x | = | 10 |