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1. For several weeks of preparation beforehand ( about December first ).
2. Children hang up the pillow case or sack.
3. It's reindeer.
4. It starts properly on 24 December.
5. Every year in Britain
b) \(\dfrac{2}{x^2+2x}+\dfrac{8-2x}{x^3+8}=\dfrac{2}{x\left(x+2\right)}+\dfrac{2}{\left(x+2\right)\left(x^2-2x+4\right)}\)\(=\dfrac{2\left(x^2-2x+4\right)}{x\left(x+2\right)\left(x^2-2x+4\right)}+\dfrac{2x}{x\left(x+2\right)\left(x^2-2x+4\right)}\)
\(=\dfrac{2x^2-4x+8+2x}{x\left(x+2\right)\left(x^2-2x+4\right)}=\dfrac{2x^2-2x+8}{x\left(x+2\right)\left(x^2-2x+4\right)}\)
c) \(\dfrac{x}{1-x^3}+\dfrac{1}{x^2+x-2}=\dfrac{-x}{x^3-1}+\dfrac{1}{x^2+2x-x-2}\)
\(=\dfrac{-x}{\left(x-1\right)\left(x^2+x+1\right)}+\dfrac{1}{x\left(x+2\right)-\left(x+2\right)}\)
\(=\dfrac{-x}{\left(x-1\right)\left(x^2+x+1\right)}+\dfrac{1}{\left(x-1\right)\left(x-2\right)}\)
\(=\dfrac{-x\left(x-2\right)}{\left(x-1\right)\left(x-2\right)\left(x^2+x+1\right)}+\dfrac{1\left(x^2+x+1\right)}{\left(x-1\right)\left(x-2\right)\left(x^2+x+1\right)}\)\(=\dfrac{-x^2+2x+x^2+x+1}{\left(x-1\right)\left(x-2\right)\left(x^2+x+1\right)}\)
\(=\dfrac{3x+1}{\left(x-1\right)\left(x-2\right)\left(x^2+x+1\right)}\)
f) \(\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}+\dfrac{3x-2}{2x-4x^2}\)
\(=\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}+\dfrac{2-3x}{2x\left(2x-1\right)}\)
\(=\dfrac{\left(1-3x\right)\left(2x-1\right)+6x^2-4x+2-3x}{2x\left(2x-1\right)}\)
\(=\dfrac{2x-1-6x^2+3x+6x^2-4x+2-3x}{2x\left(2x-1\right)}\)
\(=\dfrac{-2x+1}{2x\left(2x-1\right)}\)
\(=\dfrac{-\left(2x-1\right)}{2x\left(2x-1\right)}=\dfrac{-1}{2x}\)
h) \(\dfrac{1}{2x^2-x-1}+\dfrac{1}{6x^2+9x+3}\)
\(=\dfrac{1}{2x^2+x-2x-1}+\dfrac{1}{3\left(2x^2+3x+1\right)}\)
\(=\dfrac{1}{x\left(2x+1\right)-\left(2x+1\right)}+\dfrac{1}{3\left(2x^2+x+2x+1\right)}\)
\(=\dfrac{1}{\left(2x+1\right)\left(x-1\right)}+\dfrac{1}{3\left[x\left(2x+1\right)+\left(2x+1\right)\right]}\)
\(=\dfrac{1}{\left(2x+1\right)\left(x-1\right)}+\dfrac{1}{3\left(x+1\right)\left(2x+1\right)}\)
\(=\dfrac{3x+3+x-1}{3\left(2x+1\right)\left(x+1\right)\left(x-1\right)}\)
\(=\dfrac{4x+2}{3\left(2x+1\right)\left(x+1\right)\left(x-1\right)}=\dfrac{2}{3\left(x+1\right)\left(x-1\right)}\)
e) \(\dfrac{x}{x+2}+\dfrac{4}{x-2}+\dfrac{8x}{4-x^2}\)
\(=\dfrac{x}{x+2}+\dfrac{4}{x-2}+\dfrac{-8x}{x^2-2^2}\)
\(=\dfrac{x}{x+2}+\dfrac{4}{x-2}+\dfrac{-8x}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x^2-2x+4x+8-8x}{\left(x-2\right)\left(x+2\right)}=\dfrac{x^2-6x+8}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x^2-2x-4x+8}{\left(x-2\right)\left(x+2\right)}=\dfrac{x\left(x-2\right)-4\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{\left(x-2\right)\left(x-4\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{x-4}{x+2}\)
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16. There were many people in the theater. I couldn’t find the seat.
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17. She was very short. She couldn’t reach the tops of the high shelves.
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18. He was very disappointed. He committed a suicide.
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19. His sudden appearance gave her a great surprise. She burst out crying.
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20. I had a lot of trouble with my schoolwork. I had to ask for help.
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21. There were a lot of questions on the test. I couldn’t finish it in half an hour.
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22. The children took a large bite of sandwich. He couldn’t chew it.
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23. It was a delicious dessert. I decided to order portion.
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24. It was a strong wind. It blew down several banyan trees in this village.
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25. There were many people in the hall. We couldn’t see Professor Taylor.
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26. The atmosphere was suffocating. Nobody could resist the temptation to go to the seaside.
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27. He lives far from the office. He often gets up early to catch the bus to go to work on time.
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28. There were very few students at the extra class. It was cancelled.
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Stress:
1.
A. poem
B. father
C. lucky
D. designer
2.
A. modern
B. novel
C. musician
D. lovely
3.
A. frequent
B. special
C. curly
D. addition
4.
A. public
B. occasion
C. player
D. problem.
5.
A. effect
B. beauty
C. listen
D. brother.