\(M=\frac{3}{2}+\frac{3}{6}+\frac{3}{12}+...+\frac{3}{2021.2022}\)

    \(=3\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2021.2022}\right)\)

    \(=3\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2021}-\frac{1}{2022}\right)\)

    \(=3\left(1-\frac{1}{2022}\right)\)

    \(=3.\frac{2021}{2022}\)

    \(=\frac{6063}{2022}\)

\(\overline{ab}+\overline{ba}=11\left(a+b\right)\)

11 là số nguyên tố để 11(a+b) là số chính phương thì a+b=11

\(\Rightarrow\overline{ab}=\left\{29;38;47;56;65;74;83;92\right\}\)

1. John was sad yesterday.

2. The birds were in the cage.

3. The children were in the class.

4. My cat was on the chair.

5. I was at the theater yesterday.

6. It was foggy this morning.

7. They were at home last Sunday.

8. I was very happy yesterday.

9. There were a lot of balloons.

10. You were at the park last night.

1 his illness, he cannot come

2 her busyness, she couldn't help us

3 his illness, he tries to go to school on time

4 the bad weather, we tried to finish the work on the road

5 the bad weather, we got to the station late

6 the old house, she liked it

7 not wearing any shoes, Carol ran outside to see what was happening

8 being afraid of flying, Fiona had to get on the plane

\(x^4-8x=x\left(x^3-8\right)=x\left(x-2\right)\left(x^2+2x+4\right)\)

\(x^2-y^2-6x+9=\left(x^2-6x+9\right)-y^2=\left(x-3\right)^2-y^2=\left(x+y-3\right)\left(x-y-3\right)\)