Given the expression:
[tex]\frac{n^2+10n+21}{n^2+3n-28}-\frac{3n}{n-4}[/tex]We can express the quadratic polynomials as:
[tex]\begin{gathered} n^2+10n+21=(n+3)(n+7) \\ n^2+3n-28=(n+7)(n-4) \end{gathered}[/tex]Then:
[tex]\begin{gathered} \frac{(n+3)(n+7)}{(n+7)(n-4)}-\frac{3n}{n-4}=\frac{n+3}{n-4}-\frac{3n}{n-4} \\ \Rightarrow=\frac{n+3-3n}{n-4}=\frac{-2n+3}{n-4} \end{gathered}[/tex]