Find the real numbers $x$ that are not in the domain of

\[f(x)=\frac{1}{(x^2-6x+8)-(x^2+x-6)}.\]

tomtom Aug 20, 2023

#2**0 **

\(f(x)\) is a rational function, so an x-value that could realistically not be in the domain occurs when the denominator equals 0.

\((x^2 - 6x + 8) - (x^2 + x - 6) = 0 \\ x^2 - 6x + 8 - x^2 - x + 6 = 0 \\ -7x+14 = 0 \\ -7x = -14 \\ x = -2\)

The value of x = -2 causes the denominator to be 0, x = -2 is the only x-value not in the domain of this function!

The3Mathketeers Aug 21, 2023