\(B=\left(\dfrac{1}{x-\sqrt{x}}+\dfrac{1}{\sqrt{x}-1}\right):\dfrac{\sqrt{x}}{x-2\sqrt{x}+1}\)

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

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

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

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

A

1. What is the number of this house?
2. It's a two-hour walk.

TH1: \(\left|1-2x\right|=1-2x\)

Ta có: \(2< 1-2x< 5\)

\(\Leftrightarrow\left\{{}\begin{matrix}1-2x>2\\1-2x< 5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-2x>1\\-2x< 4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< -\dfrac{1}{2}\\x>-2\end{matrix}\right.\Leftrightarrow-2< x< -\dfrac{1}{2}\)

\(\Rightarrow x=-1\)

TH2: \(\left|1-2x\right|=-\left(1-2x\right)=2x-1\)

Ta có: \(2< 2x-1< 5\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x-1>2\\2x-1< 5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x>3\\2x< 6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>\dfrac{3}{2}\\x< 3\end{matrix}\right.\Leftrightarrow\dfrac{3}{2}< x< 3\)

\(\Rightarrow x=2\)

Vậy \(x\in\left\{-1;2\right\}\)

1. A

2. D

3. C

4. D

5. A

1. boring with -> bored with 

2. the ethnic -> an ethnic

3. closes -> closed

4. as -> than

5. to speak -> speaking

6. in -> on

7. a best -> the best

8. at -> on

25. Taro isn't interested in reading books.

26. It takes them half an hour to walk to the bus stop.

27. You should not spend time hanging out with him.

28. Girls often spend hours buying new clothes.

29. What about having a cup of tea?

30. How about going to the cinema together?

1. off

2. to

3. Both

4. about

5. missed

6. of

7. for

8. such

9. much

10. to do

13C

14B

15C

16A

17D

18A

19D

20C

\(\left|3x-4\right|=x-5\)

\(\Leftrightarrow\left[{}\begin{matrix}3x-4=x-5\\3x-4=-x+5\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=-1\\4x=9\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{2}\\x=\dfrac{9}{4}\end{matrix}\right.\)