We have the expression:
[tex]\frac{y^2-9}{y^2+y-12}[/tex]
The restricted values of y are those values that make the denominator 0. This is the same as solving the equation:
[tex]y^2+y-12=0[/tex]
This term can be factorized as:
[tex]\begin{gathered} y^2+y-12=(y+4)(y-3) \\ \Rightarrow(y+4)(y-3)=0 \end{gathered}[/tex]
This is true for y = -4 and y = 3. So the restricted values for y are:
[tex]y\ne\mleft\lbrace-4,3\mright\rbrace[/tex]
