Find all values of a that satsify the equation \frac{a}{3} + 1 = \frac{a + 3}{a} + 1.
\( \frac{a}{3} + 1 = \frac{a + 3}{a} + 1 \)
a/3 = (a + 3) / a cross-multiply
a^2 = 3(a + 3)
a^2 = 3a + 9
a^2 - 3a = 9
a^2 -3a + 9/4 = 9 + 9/4
(a - 3/2)^2 = 45 / 4 take both roots
a - 3/2 = + / - 3sqrt 5 / 2
a = [ 3 +/- 3sqrt 5 ] / 2
+782 
