Question

Solve the following equation for the unknown: `("a" - 1)/(2) - ("a" + 1)/(3)` = 5 - a

Answer 1

`("a" - 1)/(2) - ("a" + 1)/(3)` = 5 - a

⇒ `("a" - 1)/(2) - ("a" + 1)/(3)` + a = 5

Take the LCM of all the denominators, that is, 2 and 3 which is 6.
Multiply throughout by the LCM
⇒ 3(a - 1) -2(a + 1) + 6a = 30
⇒ 3a - 3 - 2a - 2 + 6a = 30
⇒ 7a = 35
⇒ a = 5.