Evaluating a Function

Algebra Level 5

The function ff from the real numbers to the real numbers satisfies f(1)=4f(1) = 4 , and

f(x+y)=(1+yx+1)f(x)+(1+xy+1)f(y)+x2y+xy+xy2, \begin{aligned} 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{aligned}

for x,y1 x, y \neq -1, x,yx, y real numbers. If f(53)=ab f \left( \frac {5}{3} \right)=\frac {a}{b} , where aa and bb are coprime positive integers, what is the value of a+ba+b?

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