a: \(A=\sqrt{\left(2025+\sqrt{2024}\right)^2}-\sqrt{2025-2\sqrt{2024}}\)
\(=2025+\sqrt{2024}-\sqrt{\left(\sqrt{2024}-1\right)^2}\)
\(=2025+\sqrt{2024}-\left(\sqrt{2024}-1\right)=2025+1=2026\)
b: \(\frac{x\cdot\sqrt{x}-1}{\left(x+\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}+\frac{x+3\sqrt{x}+5}{\sqrt{x}+2}\)
\(=\frac{\left(x+\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\left(x+\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}+\frac{x+3\sqrt{x}+5}{\sqrt{x}+2}\)
\(=\frac{\sqrt{x}-1+x+3\sqrt{x}+5}{\sqrt{x}+2_{}}=\frac{x+4\sqrt{x}+4}{\sqrt{x}+2}=\frac{\left(\sqrt{x}+2\right)^2}{\sqrt{x}+2}=\sqrt{x}+2\)
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