Let f(x)= sqrt((x/x+3)-5). Find the domain.

Answer 1

you know that x/(x+3) is undefined at x = -3

since √n is defined only for n >= 0, we need

x/(x+3)-5 >= 0
x/(x+3) > 5
x > 5x+15
-15 > 4x
-15/4 > x

So, the domain is all reals less than -15/4. Note that this automatically excludes x = -3.