| 10 | ÷ | x | + | ( | x | − | 5 | ) | ÷ | ( | x | + | 10 | ) | = | 1 |
| Multiply both sides of the equation by: | x |
| 10 | + | ( | x | − | 5 | ) | ÷ | ( | x | + | 10 | ) | × | x | = | 1 | x |
| 10 | + | x | ÷ | ( | x | + | 10 | ) | × | x | − | 5 | ÷ | ( | x | + | 10 | ) | × | x | = | 1 | x |
| Multiply both sides of the equation by: | ( | x | + | 10 | ) |
| 10 | ( | x | + | 10 | ) | + | x | x | − | 5 | x | = | 1 | x | ( | x | + | 10 | ) |
| 10 | x | + | 10 | × | 10 | + | x | x | − | 5 | x | = | 1 | x | ( | x | + | 10 | ) |
| 10 | x | + | 10 | × | 10 | + | x | x | − | 5 | x | = | 1 | x | x | + | 1 | x | × | 10 |
| 10 | x | + | 100 | + | x | x | − | 5 | x | = | 1 | x | x | + | 10 | x |
| 5 | x | + | 100 | + | x | x | = | 1 | x | x | + | 10 | x |