Step 1 :Simplify the numerator: \(5^{2}+2^{2}-1^{2} = 25+4-1 = 28\)
Step 2 :Simplify the denominator: \(8 \div 2 \cdot 9 \cdot 1 \div 9 = 4 \cdot 9 \cdot 1 \div 9 = 4\)
Step 3 :Divide the numerator by the denominator: \(\frac{28}{4} = 7\)
Step 4 :Final Answer: \(\boxed{7}\)