Giving your answer in interval notation, find the domain of the function sqrt(((x+4)(x−4))/((x−7)(x−5)))

Answer 1

√( ((x+4)(x−4)) / ((x−7)(x−5)) )

First, you need to exclude values which make the denominator zero: 5 and 7

Next, since the domain of √x is x>=0, you need

((x+4)(x−4)) / ((x−7)(x−5)) >= 0
This is true only for
x <= -4, 4<=x<5 and x>7
or
(-∞,-4]U[4,5)U(7,∞)