`***`Lời giải`***`
`A=\frac{\sqrt{a}-2}{\sqrt{a}-1}+\frac{\sqrt{a}+1}{\sqrt{a}-2}+\frac{3\sqrt{a}-4}{a-3\sqrt{a}+2}`
ĐKXĐ: `a≥0; ane1;ane4`
`=\frac{\sqrt{a}-2}{\sqrt{a}-1}+\frac{\sqrt{a}+1}{\sqrt{a}-2}+\frac{3\sqrt{a}-4}{a-\sqrt{a}-2\sqrt{a}+2}`
`=\frac{\sqrt{a}-2}{\sqrt{a}-1}+\frac{\sqrt{a}+1}{\sqrt{a}-2}+\frac{3\sqrt{a}-4}{\sqrt{a}(\sqrt{a}-1)-2(\sqrt{a}-1)}`
`=\frac{\sqrt{a}-2}{\sqrt{a}-1}+\frac{\sqrt{a}+1}{\sqrt{a}-2}+\frac{3\sqrt{a}-4}{(\sqrt{a}-1)(\sqrt{a}-2)}`
`=\frac{(\sqrt{a}-2)^2+a-1+3\sqrt{a}-4}{(\sqrt{a}-1)(\sqrt{a}-2)}`
`=\frac{a-4\sqrt{a}+4+a-1+3\sqrt{a}-4}{(\sqrt{a}-1)(\sqrt{a}-2)}`
`=\frac{2a-\sqrt{a}-1} {(\sqrt{a}-1)(\sqrt{a}-2)}`
`=\frac{2a-2\sqrt{a}+\sqrt{a}-1} {(\sqrt{a}-1)(\sqrt{a}-2)}`
`=\frac{2\sqrt{a}(\sqrt{a}-1)+\sqrt{a}-1} {(\sqrt{a}-1)(\sqrt{a}-2)}`
`=\frac{(2\sqrt{a}+1)(\sqrt{a}-1)} {(\sqrt{a}-1)(\sqrt{a}-2)}`
`=\frac{2\sqrt{a}+1} {\sqrt{a}-2}`
Vậy `A=\frac{2\sqrt{a}+1} {\sqrt{a}-2}` với `a≥0; ane1;ane4`
