What is the domain of f(x) = (x+1)/(x^2 - 7x + 12)

We have to find the domain of f(x) = (x+1)/(x^2 - 7x +
12)

The domain is the set of all values of the independent
variable x for which f(x) is defined.

f(x) = (x+1)/(x^2 -
7x + 12) is defined for all values of x except those that make x^2 - 7x + 12 = 0. When
the denominator is 0, we get a number of the form (x - 1)/0 which is
indeterminate.

x^2 - 7x + 12 =
0

=> x^2 – 4x – 3x + 12 =
0

=> x(x – 4) – 3(x – 4) =
0

=> (x – 4)(x – 3) =
0

The denominator becomes 0 when x = 4 and when x =
3

The domain of the function is R – {3,
4}