a: \(A=\dfrac{2024^3+1}{2024^2-2023}\)
\(=\dfrac{\left(2024+1\right)\left(2024^2-2024\cdot1+1^2\right)}{2024^2-2023}\)
\(=\dfrac{2025\cdot\left(2024^2+1-2024\right)}{2024^2-2023}=2025\)
b: \(B=\dfrac{\left(x+5\right)^2+\left(x-5\right)^2}{x^2+25}\)
\(=\dfrac{x^2+10x+25+x^2-10x+25}{x^2+25}\)
\(=\dfrac{2x^2+50}{x^2+25}=2\)
a)\(A=\dfrac{2024^3+1}{2024^2-2023}\)
\(\Rightarrow A=\dfrac{\left(2024+1\right)\left(2024^2-2024+1\right)}{2024^2-2024}\)
\(\Rightarrow A=\dfrac{2025\left(2024^2-2023\right)}{2024^2-2024}\)
\(\Rightarrow A=2024+1=2025\)
b) \(B=\dfrac{\left(x+5\right)^2+\left(x-5\right)^2}{x^2+25}\)
\(\Rightarrow B=\dfrac{x^2+10x+25+x^2-10x+25}{x^2+25}\)
\(\Rightarrow B=\dfrac{2x^2+50}{x^2+25}\)
\(\Rightarrow B=\dfrac{2\left(x^2+25\right)}{x^2+25}\)
\(\Rightarrow B=2\)
