Let $f:N\to Q$  be  a function, where N denotes the set of natural numbers, and Q denotes the set of rational numbers. Suppose that $f\left(1\right)=\frac{3}{2}$ , and $f(x+y)=(1+\frac{y}{x+1})f\left(x\right)+(1+\frac{x}{y+1})f\left(y\right)+x^{2}y+xy+x{y}^2$ for all natural numbers x,y.