| 3a = 3b |
(multiplying both sides by the real number) |
| 11a = 11b |
(multiplying both sides by the "real" number) |
| 3a2 = 3ab |
(multiplying by a on both sides) |
| 11ab = 11b2 |
(multiplying by b on both sides) |
| 3a2 - 11ab = 3ab - 11b2 |
(subtracting the above two equations to make one) |
| 3a2 - 3ab = 11ab - 11b2 |
(subtracting 3ab and adding 11ab to both sides) |
| 3a2 - 3ab + ab - b2 = 12ab -
12b2 |
(adding ab and subtracting b2 from both
sides) |
| 3a(a-b) + b(a-b) = 12b(a-b) |
(factoring out common factors ) |
| 3a + b = 12b |
(divide both sides by a-b) |
| 3a = 11b |
(subtracting b from both sides) |
| 3b = 11b |
(substituting a for b, remembering that they are
equal) |
| 3 = 11 |
(removing common terms) |