Step 1 :Given the expression: \(\frac{x^{2}-9 x+18}{x^{2}-5 x+6}\)
Step 2 :Factorize the numerator \(x^{2}-9 x+18\) into \((x-3)(x-6)\)
Step 3 :Factorize the denominator \(x^{2}-5 x+6\) into \((x-2)(x-3)\)
Step 4 :After factorization, the expression becomes \(\frac{(x-3)(x-6)}{(x-2)(x-3)}\)
Step 5 :Cancel out the common factors from the numerator and the denominator
Step 6 :The simplified expression is \(\boxed{\frac{x-6}{x-2}}\)