Simplify the given expression: $1-\frac{1}{x-2}-\frac{3}{x^{2}-x-2}$

Step 1 ：Given the expression: \(1-\frac{1}{x-2}-\frac{3}{x^{2}-x-2}\)

Step 2 ：We need to simplify this expression. To do this, we need to find a common denominator for all the fractions and then combine them. The common denominator in this case would be \((x-2)(x^{2}-x-2)\).

Step 3 ：By finding the common denominator and combining the fractions, we get the simplified expression: \(\frac{x^{2} - 2x - 6}{x^{2} - x - 2}\)

Step 4 ：Final Answer: The simplified form of the given expression is \(\boxed{\frac{x^{2} - 2x - 6}{x^{2} - x - 2}}\)