Find all values of a that satsify the equation \frac{a}{3} + 1 = \frac{a + 3}{a} + 1.
\(\frac{a}{3} + 1 = \frac{a + 3}{a} + 1\)
Subtract 1 from both sides: \({a\over3}={a+3\over{a}}\)
Cross multiply: \(a^2=3a+9\); \(a^2-3a-9=0\)
Use quadratic formula: \(a = {3 \pm\sqrt{9+36}\over2}={3\pm3\sqrt{5}\over2}\)
+624 
