Solve the equation.

Question

1/a-1/3=1/a-2

Answer 1

1/a - 1/3 = 1/(a-2)

 

Multiply by the LCD, 3a(a-2), to obtain:  3(a-2) - a(a-2) = 3a

 

                                                          3a - 6 - a² + 2a = 3a

 

                                                               a² - 2a + 6 = 0

 

a = [2 ± √(4-24)]/2 = [2 ± 2√5 i]/2 = 1 ± √5 i