a/ ĐK x>0 ; x\(\ne\)1
\(M=\frac{1}{\sqrt{x}\left(\sqrt{x}^3-1\right)}:\frac{\sqrt{x}+1}{\sqrt{x}\left(x+\sqrt{x}+1\right)}=\frac{\sqrt{x}\left(x+\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)\left(\sqrt{x+1}\right)\sqrt{x}}\)\(=\frac{1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}=\frac{1}{x-1}\)