Given:
[tex]\frac{5}{n-4}+\frac{4n}{n+1}[/tex]
To write as a single rational expression:
On cross multiplication we get,
[tex]\begin{gathered} \frac{5}{n-4}+\frac{4n}{n+1}=\frac{5(n+1)+4n(n-4)}{(n-4)(n+1)} \\ =\frac{5n+5+4n^2-16n}{(n-4)(n+1)} \\ =\frac{4n^2-11n+5}{n^2-4n+n-4} \\ =\frac{4n^2-11n+5}{n^2-3n-4} \end{gathered}[/tex]
Hence, the answer is,
[tex]\frac{4n^2-11n+5}{n^2-3n-4}[/tex]
