If \(f(x)=x^2-5x+6\) and \(g(x)=x-2\), what is \(\left(\frac{f}{g}\right)(x)\) for \(x\ne2\)?

Correct answer: \(x-3\)

\(\left(\frac{f}{g}\right)(x)=\frac{f(x)}{g(x)}=\frac{x^2-5x+6}{x-2}\). Factoring the numerator gives \(x^2-5x+6=(x-2)(x-3)\), so for \(x\ne2\), the quotient is \(x-3\). Option C is only the denominator, while option B has an incorrect sign. Exam tip: factor the quadratic before dividing, and exclude the value that makes the original denominator zero.