+866 Find all values of $a$ that satisfy the equation
\[\frac{a}{3} + 1 = \frac{a + 3}{a} - \frac{a^2 + 2}{a}.\]
+103 a/3 + 1 = (( a+3) - (a^2 + 2))/a
a/3 + 1 =( a^2 - a - 1 ) / a
a ( a/3 + 1 ) = a^2 - a - 1
a^2/3 + a = a^2 - a -1
a^2/3 = a^2 - 2a -1
0 = (2a^2 - 2a) / 3 - 1
then we can plug this equation into the quadratic equation,
this gives us the answer
(3+sqrt 15 )/2 or (3-sqrt15)/2
please if anyone could check my answer that would be a fire 
+128578 Assuming "a" not equal to 0, multiply through by a
a^2/3 + a = (a + 3) - (a^2 + 2)
(1/3)a^2 + a = -a^2 + a + 1 simplify as
(4/3)a^2 = 1 multiply both sides by 3/4
a^2 = 3/4 take both roots
a = sqrt (3) / 2 or a = -sqrt (3) / 2
