* Cho:

A=\(\dfrac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\dfrac{2x+\sqrt{x}}{\sqrt{x}}+\dfrac{2\left(x-1\right)}{\sqrt{x}-1}\), với x>0 và x≠1

a. Rút gọn A

b. Tìm giá trị nhỏ nhất của A

* Giải phương trình

a. \(x^2-2\sqrt{5}x+5=0\)

b. \(\sqrt{x+3}=1\)

* Cho biểu thức

M=\(\dfrac{\sqrt{x}}{\sqrt{x}-1}-\dfrac{2\sqrt{x}-1}{x-\sqrt{x}}\), với x>0 và x≠1

a. Thu gọn M

b. Giải phương trình M=2

c. So sánh M và 1

* Cho:

A= \(\left(\dfrac{\sqrt{2}+\sqrt{3}}{\sqrt{2}-\sqrt{3}}-\dfrac{\sqrt{2}-\sqrt{3}}{\sqrt{2}+\sqrt{3}}\right).\left(\dfrac{\sqrt{3}-1}{3\sqrt{2}-\sqrt{6}}\right)\)

CMR: A là số nguyên

* Giải phương trình:

a. \(x+\sqrt{x^2-4x+4}=\dfrac{1}{2}\)

b. \(\sqrt{9x^2-9}+\sqrt{4x^2-4}=\sqrt{16x^2-16}+2\)

* Tính

a. A=\(\left(\dfrac{6+\sqrt{20}}{3+\sqrt{5}}+\dfrac{\sqrt{14}-\sqrt{2}}{\sqrt{7}-1}\right):\left(2+\sqrt{2}\right)\)

b. B=\(\sqrt{5-2\sqrt{6}}+\sqrt{5+2\sqrt{6}}-\dfrac{11}{2\sqrt{3}+1}\)

* Giải phương trình

a. \(x^2-2\sqrt{5x}+5=0\)

b. \(\sqrt{x+3}=1\)

* Cho: 

A=\(\dfrac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\dfrac{2x+\sqrt{x}}{\sqrt{x}}+\dfrac{2\left(x-1\right)}{\sqrt{x}-1}\) , với x>0 và x≠1

a. Rút gọn A

b. Tìm giá trị nhỏ nhất của A

1. Tính

a. \(\left(3\sqrt{2}+2\sqrt{3}\right)\left(2\sqrt{3}-3\sqrt{2}\right)\)

b. \(\dfrac{1}{\sqrt{2013}-\sqrt{2014}}-\dfrac{1}{\sqrt{2014}-\sqrt{2015}}\)

c. \(\sqrt{\left(4+\sqrt{10}\right)^2}-\sqrt{\left(4-\sqrt{10}\right)^2}\)

d. \(\sqrt{3-2\sqrt{2}}+\sqrt{6-4\sqrt{2}}+\sqrt{9-4\sqrt{2}}\)

* Write the second sentence so that it has a similar meaning to the first. Use the passive form.
1. When did they buy this car?
………………………………………………………………………………………………………………………………
2. Jim baked this cake yesterday.
………………………………………………………………………………………………………………………………
3. When did they decorate your kitchen?
………………………………………………………………………………………………………………………………
4. They cancelled all flights because of fog.
………………………………………………………………………………………………………………………………
5. She showed her ticket to the airline agent.
………………………………………………………………………………………………………………………………
6. Tim ordered this train ticket for his mother.
………………………………………………………………………………………………………………………………
7. The board awarded the first prize to the reporter.
………………………………………………………………………………………………………………………………
8. The committee appointed Alice secretary for the meeting.
………………………………………………………………………………………………………………………………
9. They made jean cloth completely from cotton in the 18 th  century.
………………………………………………………………………………………………………………………………
10. Their grandmother told them this story when they visited her last week.
………………………………………………………………………………………………………………………………

* Complete each blank with a suitable preposition.
The word “jeans” comes (1) ………………a kind of material that was made (2) ………………Europe. The material, called jeans, was named (3) ………………sailors from Genoa in Italy, because they wore clothes made (4) ………………it. In the 18 th century jean cloth was made completely from cotton and
workers at that time loved wearing it because the material was very strong and it did not wear (5)………………easily. In the 1960s, many university and college students wore jeans. Designers made different styles of jeans to match the 1960s’ fashions: embroidered jeans, painted jeans and so (6)
………………. In the 1970s more and more people started wearing jeans because they became cheaper. In the 1980s jeans finally became high fashion clothing, when famous designers started making their own
styles of jeans, with their own labels (7) ………………them. Sales of jeans went up and (8)………………. But in the 1990s the worldwide economic situation got worse, and the sale of jeans stopped growing. However, jeans have never been (9) ………………of fashion, and today young generation is still fond (10) ………………wearing them.