\(\left(x^3y+xy^3+xy\right):y\left(x^2+y^2+1\right).\)
\(=xy.\left(x^2+y^2+1\right):y.\left(x^2+y^{2+}1\right)\)
\(=\left(xy:y\right).\left(x^2+y^2+1\right)^2\)
\(=x.\left(x^2+y^2+1\right)^2\)
\(=\frac{\left[xy\left(x^2+y^2+1\right)\right]}{y.\left(x^2+y^2+1\right)}\)
\(=x\)