The removable discontinuity of the given function is (-3, -3).
The given function are f(x)=(x²+12x+27)/(x²+4x+3).
We need to find the discontinuities of the function.
Discontinuous functions are functions that are not a continuous curve - there is a hole or jump in the graph. It is an area where the graph cannot continue without being transported somewhere else.
f(x)=(x²+12x+27)/(x²+4x+3)=(x²+9x+3x+27)/(x²+3x+x+3+
=(x+9)(x+3)/(x+3)(x+1)=(x+9)/(x+1)
The holes in the graph by factoring and cancelling are (-3, -3).
Therefore, the removable discontinuity of the given function is (-3, -3).
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