Answer:
[tex]\frac{y-4}{y+8}[/tex]
Step-by-step explanation:
Compute the given expression and simplify:
[tex]\begin{gathered} \frac{(y^2-7y+12)(y+1)}{(y+1)(y^2+5y-24)} \\ =\frac{y^2-7y+12}{y^2+5y-24} \end{gathered}[/tex]
Now, factorize and simplify the expression:
[tex]\begin{gathered} \frac{(y-3)(y-4)}{(y-3)(y+8)} \\ \text{ Eliminate like terms:} \\ =\frac{y-4}{y+8} \end{gathered}[/tex]
