$\text{ĐKXĐ:}$ `x\geq0,x\ne4,x\ne\frac{16}{9}`
`a,`
`P=\frac{2\sqrt{x}-4}{3\sqrt{x}-4}-\frac{4+2\sqrt{x}}{\sqrt{x}-2}+\frac{x+13\sqrt{x}-20}{(3\sqrt{x}-4)(\sqrt{x}-2)}`
`=\frac{(2\sqrt{x}-4)(\sqrt{x}-2)}{(3\sqrt{x}-4)(\sqrt{x}-2)}-\frac{(4+2\sqrt{x})(3\sqrt{x}-4)}{(3\sqrt{x}-4)(\sqrt{x}-2)}+\frac{x+13\sqrt{x}-20}{(3\sqrt{x}-4)(\sqrt{x}-2)}`
`=\frac{(2\sqrt{x}-4)(\sqrt{x}-2)-(4+2\sqrt{x})(3\sqrt{x}-4)+x+13\sqrt{x}-20}{(3\sqrt{x}-4)(\sqrt{x}-2)}`
`=\frac{2x-4\sqrt{x}-4\sqrt{x}+8-(12\sqrt{x}-16+6x-8\sqrt{x})+x+13\sqrt{x}-20}{(3\sqrt{x}-4)(\sqrt{x}-2)}`
`=\frac{2x-4\sqrt{x}-4\sqrt{x}+8-12\sqrt{x}+16-6x+8\sqrt{x}+x+13\sqrt{x}-20}{(3\sqrt{x}-4)(\sqrt{x}-2)}`
`=\frac{-3x+\sqrt{x}+4}{(3\sqrt{x}-4)(\sqrt{x}-2)}`
`=\frac{-3x+4\sqrt{x}-3\sqrt{x}+4}{(3\sqrt{x}-4)(\sqrt{x}-2)}`
`=\frac{-\sqrt{x}(3\sqrt{x}-4)-(3\sqrt{x}-4)}{(3\sqrt{x}-4)(\sqrt{x}-2)}`
`=\frac{(3\sqrt{x}-4)(-\sqrt{x}-1)}{(3\sqrt{x}-4)(\sqrt{x}-2)}`
`=\frac{-\sqrt{x}-1}{\sqrt{x}-2}`
Vậy với `x\geq0,x\ne4,x\ne\frac{16}{9}` thì `P=\frac{-\sqrt{x}-1}{\sqrt{x}-2}`
`b,` `P\geq-\frac{3}{4}`
`⇔\frac{-\sqrt{x}-1}{\sqrt{x}-2}\geq-\frac{3}{4}`
`⇔\frac{-\sqrt{x}-1}{\sqrt{x}-2}+\frac{3}{4}\geq0`
`⇔\frac{4(-\sqrt{x}-1)}{4(\sqrt{x}-2)}+\frac{3(\sqrt{x}-2)}{4(\sqrt{x}-2)}\geq0`
`⇔\frac{4(-\sqrt{x}-1)+3(\sqrt{x}-2)}{4(\sqrt{x}-2)}\geq0`
`⇔\frac{-4\sqrt{x}-4+3\sqrt{x}-6}{4(\sqrt{x}-2)}\geq0`
`⇔\frac{-\sqrt{x}-10}{4(\sqrt{x}-2)}\geq0`
`\sqrt{x}\geq0` với mọi `x\geq0`
`⇒-\sqrt{x}\leq0` với mọi `x\geq0`
`⇒ -\sqrt{x}-10\leq-10<0` với mọi `x\geq0`
`⇒ P\geq-\frac{3}{4}`
`⇔ 4(\sqrt{x}-2)<0`
`⇔\sqrt{x}-2<0`
`⇔\sqrt{x}<2`
`⇔x<4`
Kết hợp ĐKXĐ: `x\geq0,x\ne\frac{16}{9}`
`⇒0\leqx<4, x\ne\frac{16}{9}`
Vậy với `0\leqx<4, x\ne\frac{16}{9}` thì `P\geq-\frac{3}{4}`
