Evaluating a Function
Algebra
Level
5
The function \(f\) from the real numbers to the real numbers satisfies \(f(1) = 4 \), and
\[ \begin{align} f(x+y) = & \left(1 + \frac {y}{x+1}\right) f(x) + \left(1 + \frac {x}{y+1} \right) f(y) \\ & + x^2y + xy + xy^2, \end{align}\]
for \( x, y \neq -1\), \(x, y\) real numbers. If \( f \left( \frac {5}{3} \right)=\frac {a}{b} \), where \(a\) and \(b\) are coprime positive integers, what is the value of \(a+b\)?
by
Calvin Lin