g: \(=\dfrac{x^2+2x-x^2-4x-2x+4}{x\left(x-2\right)\left(x+2\right)}=\dfrac{-4x+4}{x\left(x-2\right)\left(x+2\right)}\)

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

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

\(e,=\dfrac{1}{x-1}-\dfrac{2x}{\left(x^2+1\right)\left(x-1\right)}=\dfrac{x^2-2x+1}{\left(x^2+1\right)\left(x-1\right)}=\dfrac{\left(x-1\right)^2}{\left(x^2+1\right)\left(x-1\right)}=\dfrac{x-1}{x^2+1}\\ f,=\dfrac{3x-1}{2\left(3x+1\right)}+\dfrac{3x+1}{2\left(3x-1\right)}-\dfrac{6x}{\left(3x-1\right)\left(3x+1\right)}\\ =\dfrac{9x^2-6x+1+9x^2+6x+1-12x}{2\left(3x-1\right)\left(3x+1\right)}=\dfrac{2\left(3x-1\right)^2}{2\left(3x-1\right)\left(3x+1\right)}=\dfrac{3x-1}{3x+1}\)

\(g,=\dfrac{x}{x\left(x-2\right)}-\dfrac{x^2+4x}{x\left(x-2\right)\left(x+2\right)}-\dfrac{2}{x\left(x+2\right)}\\ =\dfrac{x^2+2x-x^2-4x-2x+4}{x\left(x-2\right)\left(x+2\right)}=\dfrac{-4x+4}{x\left(x-2\right)\left(x+2\right)}\\ h,=\dfrac{2x^2+1-x^2+1-x^2+x-1}{\left(x+1\right)\left(x^2-x+1\right)}=\dfrac{x+1}{\left(x+1\right)\left(x^2-x+1\right)}=\dfrac{1}{x^2-x+1}\)

a/ Tam giác AMN cân tại A (gt). \(\Rightarrow\) \(\widehat{AMN}=\widehat{ANM};AM=AN.\)

Xét tam giác AMB và tam giác ANC có:

+ AM = AN (cmt).

+ \(\widehat{AMB}=\widehat{ANC}\left(\widehat{AMN}=\widehat{ANM}\right).\)

+ MB = NC (gt).

\(\Rightarrow\) Tam giác AMB = Tam giác ANC (c - g - c).

\(\Rightarrow\) AB = AC (cặp cạnh tương ứng).

Xét tam giác ABC có: AB = AC (cmt).

\(\Rightarrow\) Tam giác ABC cân tại A.

b/ Tam giác ABC cân tại A (cmt) \(\Rightarrow\) \(\widehat{ABC}=\widehat{ACB}.\)

Mà \(\widehat{ABC}=\widehat{MBH;}\widehat{ACB}=\widehat{NCK}\text{​​}\) (đối đỉnh).

\(\Rightarrow\) \(\widehat{MBH}=\widehat{NCK}.\)

Xét tam giác MBH và tam giác NCK \(\left(\widehat{BHM}=\widehat{CKN}=90^o\right)\)có:

+ MB = NC (gt).

+ \(\widehat{MBH}=\widehat{NCK}\left(cmt\right).\)

\(\Rightarrow\) Tam giác MBH = Tam giác NCK (cạnh huyền - góc nhọn).

c/ Tam giác MBH = Tam giác NCK (cmt).

\(\Rightarrow\) \(\widehat{BMH}=\widehat{CNK}\) (cặp góc tương ứng).

Xét tam giác OMN có: \(\widehat{NMO}=\widehat{MNO}\) (do \(\widehat{BMH}=\widehat{CNK}\)).

\(\Rightarrow\) Tam giác OMN tại O.

postponed

is

will die

rains

doesn't hurry

don't finish

lied

was repaired

changing

doesn't started

pollute

will be

are

littered

5: \(=\dfrac{1}{2}\cdot10-\dfrac{1}{2}=\dfrac{1}{2}\cdot9=\dfrac{9}{2}\)

\(1)15-3x=0.\\ \Leftrightarrow3x=15.\\ \Leftrightarrow x=5.\)

\(2)4x+12=2x\left(x+3\right).\\ \Leftrightarrow4\left(x+3\right)-2x\left(x+3\right)=0.\\ \Leftrightarrow\left(4-2x\right)\left(x+3\right)=0.\) 

\(\Leftrightarrow\left[{}\begin{matrix}4-2x=0.\\x+3=0.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=2.\\x=-3.\end{matrix}\right.\)

\(3)\dfrac{1}{x-1}+\dfrac{2x^2-5}{x^3-1}=\dfrac{4}{x^2+x+1}.\left(x\ne1\right).\\ \Leftrightarrow\dfrac{x^2+x+1+2x^2-5-4x+4}{\left(x-1\right)\left(x^2+x+1\right)}=0.\\ \Rightarrow3x^2-3x=0.\\ \Leftrightarrow3x\left(x-1\right)=0.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(TM\right).\\x=1\left(koTM\right).\end{matrix}\right.\)

1A

2B =)

Exercise 1:

1. will give

2. would type

3. would have visited

4. attended

5. knew

6. had arrived

7. wouldn't make

8. were

9. find

10. were

Exercise 2:

1. If you don't keep silent, you'll wake the baby up.

2. If you stop talking, you will understand the lesson.

3. If I knew her number, I would ring her up.

4. If I knew the answer, I could tell you.

5. If we had had a map, we wouldn't have got lost.

6. If Susan hadn't eaten four cream cakes, she wouldn't have felt sick.

7. If you hadn't been for this treatment, the patient would have died.

8. If he hadn't been late everyday, he wouldn't have lost his job.

9. If Peter didn't eat so many chips, he wouldn't be fat.

10. If Robert hadn't started smoking cigarettes, he wouldn't have got a bad cough.

Exercise 3:

1. Unless you like this one, I'll bring you another.

2. Unless she hurries, she'll be late.

3. Unless you are careful, you'll cut yourshelf.

4. Unless you had sneezed, he wouldn't have known that we were there.

Exercise 4:

1. D

2. B

3. C

4. B

5. C

30. c

1. c

2. b

3. d

4. b

5. a

6. c

Exercise 5:

7. If he didn't have to study for exam, he could go out.

8. If she weren't lazy, she could pass the exam.

9. If he pays me tonight, I will have enough money to buy a car.

10. If he didn't smoke too much, he could get rid of his cough.

11. If she weren't very shy, she would enjoy the party.

12. If I get a work permit I will stay for another month.

13. If he were so healthy, he would take some exercises.

14. If I had the right change, we could get the ticket.

15. If you don't study hard, you will pass the exam.

16. If you are impatient, you will make mistakes.

17. If I had eaten lunch, I wouldn't feel hungry now.

18. Unless they invite me, I won't come.

19. If he had revised all his lessons, he wouldn't have failed the exam.

20. If you walk to the park, it will take you 5 minutes.  

21. Unless you leave me alone, I'll call the police.

. Câu bị động với modal verbs

1. A new computer will be bought by Jane.

2. It won't be done.

3. The new film won't be showed.

4. He won't be asked.

5. The car won't be repaired by William.

6. A question will be asked.

7. You will be helped by his father tomorrow.

8. The meeting will be held.

9. This machine musn't be used.

10. His parents will be visited by Tom next month.

12. The test must be finished before ten.

13. Tea can't be made with cold water.

14. Our teeth should be cleaned twice a day.

15. The secretary will be phoned by the manager this morning.

4. Câu bị động với thì hiện tại hoàn thành

1. The bill has been paid by Nancy.

2. A hamburger has been eaten.

3. The present has been opened.

4. The cats had been fed by Ann. (Đây là thì Quá khứ hoàn thành)

5. The book hasn't been read.

6. Letter hasn't been sent.

7. The thieves haven't been caught.

8. Our homework has been done.

9. An email has been written by my friend for 2 hours.

10. Their work had been finished.

11. The English grammar has been explained by our teachers.