Đáp án:
Giải thích các bước giải:
1) `P=\frac{\sqrt{x}-1}{2-\sqrt{x}}`
ĐK: `x \ge 0, x \ne 4`
`P=1 1/4`
`⇔ \frac{\sqrt{x}-1}{2-\sqrt{x}}=1 1/4`
`⇔ \frac{\sqrt{x}-1}{2-\sqrt{x}}=5/4`
`⇔ 5(2-\sqrt{x})=4(\sqrt{x}-1)`
`⇔ 10-5\sqrt{x}=4\sqrt{x}-4`
`⇔ 14=9\sqrt{x}`
`⇔ \sqrt{x}=14/9`
`⇔ x=196/81\ (TM)`
Vậy `x=196/81` thì `P= 1 1/4`
2) `Q=(\frac{x}{x-1}+\frac{\sqrt{x}+1}{1-\sqrt{x}}):\frac{2\sqrt{x}+1}{\sqrt{x}+1}`
ĐK: `x \ge 0, x \ne 1`
`Q=[\frac{x}{(\sqrt{x}-1)(\sqrt{x}+1)}-\frac{(\sqrt{x}+1)^2}{(\sqrt{x}-1)(\sqrt{x}+1)}].\frac{\sqrt{x}+1}{2\sqrt{x}+1}`
`Q=[\frac{x-x-2\sqrt{x}-1}{(\sqrt{x}-1)(\sqrt{x}+1)}].\frac{\sqrt{x}+1}{2\sqrt{x}+1}`
`Q=\frac{-2\sqrt{x}-1}{(\sqrt{x}-1)(\sqrt{x}+1)}.\frac{\sqrt{x}+1}{2\sqrt{x}+1}`
`Q=\frac{-(2\sqrt{x}+1)}{(\sqrt{x}-1)(\sqrt{x}+1)}.\frac{\sqrt{x}+1}{2\sqrt{x}+1}`
`Q=\frac{-1}{\sqrt{x}-1}`
3) `P.Q=\frac{\sqrt{x}}{m-3\sqrt{x}}`
`⇔ \frac{\sqrt{x}-1}{2-\sqrt{x}}.\frac{-1}{\sqrt{x}-1}=\frac{\sqrt{x}}{m-3\sqrt{x}}`
`⇔ \frac{-1}{2-\sqrt{x}}=\frac{\sqrt{x}}{m-3\sqrt{x}}`
`⇔ -m+3\sqrt{x}=2\sqrt{x}-x`
`⇔ \sqrt{x}(\sqrt{x}+1)=m`
Vậy với `m=x+\sqrt{x}` thì TM `P.Q=\frac{\sqrt{x}}{m-3\sqrt{x}}`
