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 \(a+b\)?

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