Solve

Let's simplify:

$\frac{a}{3}+1=1+\frac{3}{a}-a+\frac{2}{a}$

$a-\frac{5}{a}+\frac{a}{3}=0$

I just put this on a calculator and got a = $\frac{\sqrt 15}{2}$, $\frac{-\sqrt 15}{2}$

I didn't know what to do.

Answer: (sqrt 15)/2, -(sqrt 15)/2

Simplify as

(a + 3) / 3 =    [ -a^2 + a + 1 ] /  a             cross-multiply

a ( a + 3)  =  3 (-a^2 + a + 1)

a^2 + 3a   = -3a^2 + 3a + 3

4a^2  = 3

a^2  = 3/4                 take both roots

a = sqrt (3)  / 2          or     a =   -sqrt (3)  / 2