a) Rút gọn A :
`A=1/(\sqrt{5}+2)-\sqrt{9+4\sqrt{5}}`
`=1/(\sqrt{5}+2)-\sqrt{4+4\sqrt{5}+5}`
`=1/(\sqrt{5}+2)-\sqrt{(2+\sqrt{5})^{2}}`
`=1/(\sqrt{5}+2)-|\sqrt{5}+2|`
`=1/(\sqrt{5}+2)-(\sqrt{5}+2)`
`=(1-(\sqrt{5}+2)^{2})/(\sqrt{5}+2)`
`=(1-5-4\sqrt{5}-4)/(\sqrt{5}+2)`
`=(-8-4\sqrt{5})/(\sqrt{5}+2)`
`=(-4(2+\sqrt{5}))/(2+\sqrt{5})`
`=-4`
+ Rút gọn B :
`B=\sqrt{x}/(\sqrt{x}-1)-(2\sqrt{x}-1)/(x-\sqrt{x})`
`=\sqrt{x}/(\sqrt{x}-1)-(2\sqrt{x}-1)/(\sqrt{x}(\sqrt{x}-1))`
`=(x-2\sqrt{x}+1)/(\sqrt{x}(\sqrt{x}-1))`
`=(\sqrt{x}-1)^{2}/(\sqrt{x}(\sqrt{x}-1))`
`=(\sqrt{x}-1)/\sqrt{x}`
b) `B<A`
`->(\sqrt{x}-1)/\sqrt{x}<-4`
`->(\sqrt{x}-1)/\sqrt{x}+4<0`
`->(\sqrt{x}-1+4\sqrt{x})/\sqrt{x}<0`
`->(5\sqrt{x}-1)/\sqrt{x}<0`
Vì `\sqrt{x}ge0`
`->5\sqrt{x}-1<0`
`->5\sqrt{x}<1`
`->\sqrt{x}<1/5`
`->x<1/25``(TM)`
Vậy `x<1/25` thì `B<A`
