Step 1 :Given the expression: \(\frac{2 x+10}{x^{2}-4 x+4}+\frac{x^{2}-25}{x-2}\)
Step 2 :Factorize the numerator and denominator of each fraction.
Step 3 :Simplify the expression by cancelling out common factors if any.
Step 4 :The expression simplifies to: \(\frac{x^{3} - 2x^{2} - 23x + 60}{x^{2} - 4x + 4}\)
Step 5 :This is the simplest form of the expression.
Step 6 :Final Answer: \(\boxed{\frac{x^{3} - 2x^{2} - 23x + 60}{x^{2} - 4x + 4}}\)