a) \(x\sqrt{x}+\sqrt{x}-x-1\)
\(=\sqrt{x}\left(x+1\right)-\left(x+1\right)\)
\(=\left(\sqrt{x}-1\right)\left(x+1\right)\)
b) \(x-1-2\sqrt{x-1}-2\)
\(=\left(\sqrt{x-1}\right)^2-2\sqrt{x-1}+1-3\)
\(=\left(\sqrt{x-1}-1\right)^2-\left(\sqrt{3}\right)^2\)
\(=\left(\sqrt{x-1}-1-\sqrt{3}\right)\left(\sqrt{x-1}-1+\sqrt{3}\right)\)