What are the restrictions on the domain of 5/x²+7x+12?

Assuming that the equation is:

Then the restriction is x cannot be 0, as the denominator of the first term can't be 0.

However, it is more likely that the equation is

And so you'd need to factorise it so it becomes

Similar to above, the denominator can't be 0, hence in this case the restriction is that x cannot be -3 or -4, as either value will lead to 0 on the bottom. All other x values can be accepted.

Hope this helped.