6
135
${\frac{{\text{ }1}}{{x}}+\frac{{1}}{{y}}=\frac{{1}}{{n!}}}\\$${\frac{{1}}{{x}}=\frac{{1}}{{n!}}-\frac{{1}}{{y}}}\\$${x=\frac{{n!y}}{{y-n!}}}\\$${\text{设}y=n!+k}\\$${\text{化}\text{简}\text{得}\text{ }x=\frac{{n!n!}}{{k}}+n!}$$\end{array}}\]$