we are given
![((x+4))/(-3x^2+12x+36)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/jaz9j0qy3hb9y5v1unz5e9d5yslvts4ry6.png)
we know that
values of x excluded when that value of x makes f(x) undefined
and any function is undefined when it's denominator becomes 0
so, we set denominator =0
and then we solve for x
![-3x^2+12x+36=0](https://img.qammunity.org/2019/formulas/mathematics/middle-school/7os0ornuy29oyc9djn37qm5q50z2fy1mw5.png)
we can factor out
![-3(x^2-4x-12)=0](https://img.qammunity.org/2019/formulas/mathematics/middle-school/dp3a735g5hu4gfrom8baljp0ti6uiciob0.png)
![(x^2-4x-12)=0](https://img.qammunity.org/2019/formulas/mathematics/middle-school/fasor1fai1wkxekhdcxlu8b9ofyqn7150z.png)
![(x-6)(x+2)=0](https://img.qammunity.org/2019/formulas/mathematics/middle-school/sjgdxvdwoggqts4iuonljbtpl4z6i4x2yr.png)
we get
![(x-6)=0](https://img.qammunity.org/2019/formulas/mathematics/middle-school/dfe56gqhwaxfivgtw8jwslhigt0kmj5vd0.png)
![x=6](https://img.qammunity.org/2019/formulas/mathematics/high-school/pcw7ukmhvd40f93rpy6r6h8i9vizrbu9zl.png)
![(x+2)=0](https://img.qammunity.org/2019/formulas/mathematics/high-school/lh96sfomozk5z6toegsouzbxb5ed7akjs5.png)
![x=-2](https://img.qammunity.org/2019/formulas/mathematics/college/th5qag8u7vhunw9k8qg5ggn9n9uidfb1gt.png)
so, excluded values are
..............Answer