\(c,P=\dfrac{1}{3}\\ \Leftrightarrow\dfrac{\sqrt{x}-1}{\sqrt{x}+1}=\dfrac{1}{3}\\ \Leftrightarrow3\sqrt{x}-3=\sqrt{x}+1\\ \Leftrightarrow2\sqrt{x}=4\\ \Leftrightarrow\sqrt{x}=2\\ \Leftrightarrow x=4\)

\(d,\) Ta có:

\(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}=\dfrac{\sqrt{x}+1-2}{\sqrt{x}+1}=1-\dfrac{2}{\sqrt{x}+1}\)

\(P\) nguyên \(\Leftrightarrow\dfrac{\sqrt{x}-1}{\sqrt{x}+1}\) nguyên

\(\Leftrightarrow\dfrac{2}{\sqrt{x}+1}\) nguyên \(\Leftrightarrow\sqrt{x}+1\inƯ\left(2\right)=\left\{\pm2;\pm1\right\}\)

Ta có bảng sau:

Vậy \(P\) nguyên \(\Leftrightarrow x=1\)

\(b.P< \dfrac{1}{2}\\ \Leftrightarrow\dfrac{\sqrt{x}-1}{\sqrt{x}+1}< \dfrac{1}{2}\\ \Leftrightarrow2\sqrt{x}-2< \sqrt{x}+1\\ \Leftrightarrow\sqrt{x}< 3\\ \Leftrightarrow x< 9\)

Vậy \(P< \dfrac{1}{2}\Leftrightarrow0\le x< 9\) và \(x\ne1\)

\(a,P=\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{2\sqrt{x}}{x\sqrt{x}-x+\sqrt{x}-1}\right):\left(\dfrac{x+\sqrt{x}}{x\sqrt{x}+x+\sqrt{x}+1}+\dfrac{1}{x+1}\right)\\ =\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{2\sqrt{x}}{x\left(\sqrt{x}-1\right)+\left(\sqrt{x}-1\right)}\right):\left(\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{x\left(\sqrt{x}+1\right)+\left(\sqrt{x}+1\right)}+\dfrac{1}{x+1}\right)\\ =\left(\dfrac{1}{\sqrt{x-1}}-\dfrac{2\sqrt{x}}{\left(x+1\right)\left(\sqrt{x}-1\right)}\right):\left(\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\left(x+1\right)\left(\sqrt{x}+1\right)}+\dfrac{1}{x+1}\right)\\ =\left(\dfrac{x+1-2\sqrt{x}}{\left(x+1\right)\left(\sqrt{x}-1\right)}\right):\left(\dfrac{\sqrt{x}+1}{x+1}\right)\\ =\dfrac{\left(\sqrt{x}-1\right)^2}{\left(x+1\right)\left(\sqrt{x}-1\right)}.\dfrac{x+1}{\sqrt{x}+1}\\ =\dfrac{\sqrt{x}-1}{\sqrt{x}+1}\)

When you go through customs, your bag may be checked by a costoms officer

Miss Brown designs clothes for ladies. She is a fashion designer.

\(a,A=\sqrt{\left(a-b\right)^2\left(a^2-b\right)^2}\\ =\left|a-b\right|\left|a^2-b\right|\)

\(b,B=\dfrac{ab+2\sqrt{b}}{3\sqrt{b}}.\dfrac{3\sqrt{b}}{ab-2\sqrt{b}}\\ =\dfrac{ab+2\sqrt{b}}{ab-2\sqrt{b}}\\ =-1\)

Sentence transformation

1. Lan is not good at learning languages.

=> Lan learns languages badly.

2. She looked young and pretty.

=> She is young and pretty.

Không nên uống sữa đậu nành trong trường hợp nào sau đây ?

A. Ăn kèm trứng gà đun sôi

B. Ăn cùng với cam, quýt

C. Khi đang rất đói

D. Đáp án A, B, C

Choose the word which is pronounced differently from the others.

A. stressed

B. tense

C. concentrate

D. self-aware

a là 0 hoặc 1