Simplify the given expression:
$\frac{x^{2}-9 x+18}{x^{2}-5 x+6}$

Answer

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Answer

The simplified expression is $\boxed{\frac{x-6}{x-2}}$

Steps

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 $\boxed{\frac{x-6}{x-2}}$