i have this problem that goes: show that
(n+1)p_{n+1} (x)-xp_{n+1}^{'} = x(np_{n} (x)-xp_{n}^{'}(x))-p_{n-1}
where
(n+1)p_{n+1}(x)=(2n+1)xp_{n}(x)-np_{n-1}(x).................(a)
i recalled a relation that says p_{n+1}^{'}-p_{n-1}^{'}=(2n+1)p_{n}
and i substituted it in equation (a) above,which gives
(n+1)p_{n+1}(x)=x(p_{n+1}^{'}-p_{n-1}^{'})-np_{n-1}(x)
rearranging, i have
(n+1)p_{n+1}(x)-xp_{n+1}^{'}=-xp_{n-1}^{'}-np_{n-1}(x)
there exit a relation also of this kind: p_{n}^{'}=xp_{n-1}^{'}+np_{n-1}
substituting, the equation now becomes
(n+1)p_{n+1}(x)-xp_{n+1}^{'}=-p_{n}

pls i need help at this point to enable me know where i got it wrong. thanks