## difference equations/recurrance relation problem

I am trying to solve the recurrance relation: $(n+1)x_{n}=nx_{n-1}+2$ with the condition that $x_{0}=3$ Does anyone know how I can get the solution given that is $x_{n}=2+\frac{1}{n+1}$ I have tried various ways but none seem to work. I will update this post with my working soon to see if anyone can ellaborate or finish off what I have started many thanks!!.