(3)) \( \frac{n^{2}+1}{n^{2}-5 n-36} \)

To simplify the expression \( \frac{n^{2}+1}{n^{2}-5 n-36} \), we can start by factoring the denominator. The denominator \( n^{2}-5n-36 \) can be factored as \( (n-9)(n+4) \), since these two factors multiply to give \( n^2 - 5n - 36 \). Thus, we can rewrite the expression as: \[ \frac{n^{2}+1}{(n-9)(n+4)} \] Now we see that the numerator \( n^2 + 1 \) does not factor nicely over the real numbers, nor does it simplify with the denominator. Therefore, the expression remains as \[ \frac{n^{2}+1}{(n-9)(n+4)} \] This fraction can be useful in various mathematical scenarios, including calculus or algebraic simplifications, but in its simplest form, this is where we stand!