Ta có : \(\sqrt{a+2\sqrt{a-1}}-\sqrt{a+8+6\sqrt{a-1}}\)
\(=\sqrt{\left(a-1\right)+2\sqrt{a-1}+1}-\sqrt{\left(a-1\right)+2.3.\sqrt{a-1}+9}\)
\(=\sqrt{\left(\left(\sqrt{a-1}\right)+1\right)^2}-\sqrt{\left(\left(\sqrt{a-1}\right)+3\right)^2}\)
\(=\sqrt{a-1}+1-\sqrt{a-1}-3=-2\)