=>1-0,5

=>0,5

\(1-\left(\frac{2}{5}+\frac{1}{10}\right)=1-\left(\frac{4}{10}+\frac{1}{10}\right)=1-\frac{1}{2}=\frac{1}{2}\)

B

B

1. What has Jim recently experienced ?

2. where do the ethnic minorities in Viet Nam often live ?

3. How are their costumes ?

4. Where do they often gather in special occasions ?

5. What does the chief of the community often tell at the communal house ?

6. When do ethnic people often hold festival ?

bạn giúp mk câu này vs ạ

https://hoc24.vn/cau-hoi/speaking-in-about-2-minutes-youimagine-that-your-class-is-going-to-throw-a-party-decide-which-type-of-food-is-suitable-for-the-party.1664754098434

Lời giải:
Ta có:

$10\equiv -1\pmod {11}$

$\Rightarrow 10^{2022}\equiv (-1)^{2022}\equiv 1\pmod {11}$

$\Rightarrow A=10^{2022}-1\equiv 1-1\equiv 0\pmod {11}$

Vậy $A\vdots 11$

ok

A= 10^2022-1

Ta có thể thấy 10^2022=100000000...........0000000000 

 10000000.......0000000000-1 thì lúc nnày tổng bằng

9999999999999999........................999999999999999999999

mà 99999999999999999999999....................9999999999999999999chia hết cho 11 nên tổng này chia hết cho 11

a: \(\frac{-2x+3}{5xy}+\frac{3x-4}{5xy}\)

\(=\frac{-2x+3+3x-4}{5xy}=\frac{x-1}{5xy}\)

b: \(\frac{x\left(x-2\right)}{x-3}+\frac{3}{3-x}\)

\(=\frac{x^2-2x-3}{x-3}\)

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

c: \(\frac{2x+7}{3\left(x+2\right)}-\frac{x+5}{3\left(x+2\right)}\)

\(=\frac{2x+7-x-5}{3\left(x+2\right)}\)

\(=\frac{x+2}{3\left(x+2\right)}=\frac13\)

d: \(\frac{5}{2x+6}+\frac{3}{x^2-9}\)

\(=\frac{5}{2\left(x+3\right)}+\frac{3}{\left(x-3\right)\left(x+3\right)}\)

\(=\frac{5\left(x-3\right)+6}{2\left(x-3\right)\left(x+3\right)}=\frac{5x-9}{2\left(x-3\right)\left(x+3\right)}\)

e: \(\frac{3x}{x+2}+\frac{x+3}{x^2-4}\)

\(=\frac{3x\left(x-2\right)+x+3}{\left(x-2\right)\left(x+2\right)}=\frac{3x^2-6x+x+3}{\left(x-2\right)\left(x+2\right)}\)

\(=\frac{3x^2-5x+3}{\left(x-2\right)\left(x+2\right)}\)

f: \(\frac{3x+2}{\left(x+2\right)^2}-\frac{1}{x+2}\)

\(=\frac{3x+2-\left(x+2\right)}{\left(x+2\right)^2}=\frac{2x}{\left(x+2\right)^2}\)

\(\frac{9}{10!}+\frac{10}{11!}+...+\frac{999}{1000!}\)

= \(\frac{1}{9!}-\frac{1}{10!}+\frac{1}{10!}-\frac{1}{11!}+...+\frac{1}{999!}-\frac{1}{100!}\)

= \(\frac{1}{9!}-\frac{1}{1000!}\)< \(\frac{1}{9!}\)( dpcm )

A = 9/10! + 9/11! + 9/12! + ...... + 9/1000! < 9/10! + 10/11! + 11/12! + ... + 999/1000! = B
9/10! = 1/9! - 1/10!
10/11! = 1/10! - 1/11!
...
999/1000! = 1/999! - 1/1000!
=> B = 1/9! - 1/1000! < 1/9!
=> A < 1/9! (dpcm)

x= 3/20

4/30

Bài 16:

1: \(\frac{\sqrt{x}+2}{\sqrt{x}-3}-\frac{\sqrt{x}+1}{\sqrt{x}-2}-3\cdot\frac{\sqrt{x}-1}{x-5\sqrt{x}+6}\)

\(=\frac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)-\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)-3\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)

\(=\frac{x-4-\left(x-2\sqrt{x}-3\right)-3\sqrt{x}+3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)

\(=\frac{x-3\sqrt{x}-1-x+2\sqrt{x}+3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}=\frac{-\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}=\frac{-1}{\sqrt{x}-3}\)

2: \(\frac{\sqrt{x}-3}{\sqrt{x}-2}-\frac{2\sqrt{x}-1}{\sqrt{x}-1}+\frac{x-2}{x-3\sqrt{x}+2}\)

\(=\frac{\left(\sqrt{x}-3\right)\left(\sqrt{x}-1\right)-\left(2\sqrt{x}-1\right)\left(\sqrt{x}-2\right)+x-2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{x-4\sqrt{x}+3-\left(2x-5\sqrt{x}+2\right)+x-2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{2x-4\sqrt{x}+1-2x+5\sqrt{x}-2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}=\frac{\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}=\frac{1}{\sqrt{x}-2}\)

3: \(\frac{3\sqrt{x}+2}{2\sqrt{x}-1}+\frac{\sqrt{x}-1}{\sqrt{x}+4}-\frac{x-6\sqrt{x}+5}{2x+7\sqrt{x}-4}\)

\(=\frac{\left(3\sqrt{x}+2\right)\left(\sqrt{x}+4\right)+\left(\sqrt{x}-1\right)\left(2\sqrt{x}-1\right)-x+6\sqrt{x}-5}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+4\right)}\)

\(=\frac{3x+14\sqrt{x}+8+2x-3\sqrt{x}+1-x+6\sqrt{x}-5}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+4\right)}=\frac{4x+17\sqrt{x}+4}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+4\right)}\)

\(=\frac{\left(4\sqrt{x}+1\right)\left(\sqrt{x}+4\right)}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+4\right)}=\frac{4\sqrt{x}+1}{2\sqrt{x}-1}\)

4: \(\frac{\sqrt{x}+4}{1-7\sqrt{x}}+\frac{\sqrt{x}-2}{\sqrt{x}+1}+\frac{24\sqrt{x}}{7x+6\sqrt{x}-1}\)

\(=\frac{-\left(\sqrt{x}+4\right)\left(\sqrt{x}+1\right)+\left(\sqrt{x}-2\right)\left(7\sqrt{x}-1\right)+24\sqrt{x}}{\left(7\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)

\(=\frac{-x-5\sqrt{x}-4+7x-15\sqrt{x}+2+24\sqrt{x}}{\left(7\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\frac{6x+4\sqrt{x}-2}{\left(7\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)

\(=\frac{\left(\sqrt{x}+1\right)\left(6\sqrt{x}-2\right)}{\left(7\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\frac{6\sqrt{x}-2}{7\sqrt{x}-1}\)

5: \(\frac{\sqrt{x}-3}{2-\sqrt{x}}+\frac{\sqrt{x}-2}{3+\sqrt{x}}-\frac{9-x}{x+\sqrt{x}-6}\)

\(=\frac{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)+\left(\sqrt{x}-2\right)^2+x-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{9-x+x-9+\left(\sqrt{x}-2\right)^2}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}=\frac{\left(\sqrt{x}-2\right)^2}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}=\frac{\sqrt{x}-2}{\sqrt{x}+3}\)

6: \(\frac{3-\sqrt{x}}{5\sqrt{x}+7}+\frac{3\sqrt{x}+4}{3\sqrt{x}-2}-\frac{42\sqrt{x}+34}{15x+11\sqrt{x}-14}\)

\(=\frac{\left(-\sqrt{x}+3\right)\left(3\sqrt{x}-2\right)+\left(3\sqrt{x}+4\right)\left(5\sqrt{x}+7\right)-42\sqrt{x}-34}{\left(5\sqrt{x}+7\right)\left(3\sqrt{x}-2\right)}\)

\(=\frac{-3x+11\sqrt{x}-6+15x+41\sqrt{x}+28-42\sqrt{x}-34}{\left(5\sqrt{x}+7\right)\left(3\sqrt{x}-2\right)}=\frac{12x+10\sqrt{x}-12}{\left(5\sqrt{x}+7\right)\left(3\sqrt{x}-2\right)}\)

\(=\frac{12x-8\sqrt{x}+18\sqrt{x}-12}{\left(5\sqrt{x}+7\right)\left(3\sqrt{x}-2\right)}=\frac{\left(3\sqrt{x}-2\right)\left(4\sqrt{x}+6\right)}{\left(5\sqrt{x}+7\right)\left(3\sqrt{x}-2\right)}=\frac{4\sqrt{x}+6}{5\sqrt{x}+7}\)

7: \(\frac{\sqrt{x}+2}{-\sqrt{x}+2}+\frac{3\sqrt{x}-4}{2\sqrt{x}-3}+\frac{-7\sqrt{x}+10}{-2x+7\sqrt{x}-6}\)

\(=\frac{\left(-\sqrt{x}-2\right)\left(2\sqrt{x}-3\right)+\left(3\sqrt{x}-4\right)\left(\sqrt{x}-2\right)+7\sqrt{x}-10}{\left(2\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{-2x-\sqrt{x}+6+3x-10\sqrt{x}+8+7\sqrt{x}-10}{\left(2\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}=\frac{x-4\sqrt{x}+4}{\left(2\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{\left(\sqrt{x}-2\right)^2}{\left(2\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}=\frac{\sqrt{x}-2}{2\sqrt{x}-3}\)

8: \(-\frac{7\sqrt{x}+7}{5\sqrt{x}-1}+\frac{2\sqrt{x}-2}{\sqrt{x}+2}+\frac{39\sqrt{x}+12}{5x+9\sqrt{x}-2}\)

\(=\frac{-\left(7\sqrt{x}+7\right)\left(\sqrt{x}+2\right)+\left(2\sqrt{x}-2\right)\left(5\sqrt{x}-1\right)+39\sqrt{x}+12}{\left(5\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)

\(=\frac{-7x-21\sqrt{x}-14+10x-12\sqrt{x}+2+39\sqrt{x}+12}{\left(5\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}=\frac{3x+6\sqrt{x}}{\left(5\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}=\frac{3\sqrt{x}}{5\sqrt{x}-1}\)

9: \(\frac{-5\sqrt{x}+4}{3\sqrt{x}-2}+\frac{6\sqrt{x}+4}{2\sqrt{x}+3}+\frac{29\sqrt{x}-28}{3\left(6x+5\sqrt{x}-6\right)}\)

\(=\frac{\left(-5\sqrt{x}+4\right)\left(2\sqrt{x}+3\right)+\left(6\sqrt{x}+4\right)\left(3\sqrt{x}-2\right)}{\left(3\sqrt{x}-2\right)\left(2\sqrt{x}+3\right)}+\frac{29\sqrt{x}-28}{3\left(3\sqrt{x}-2\right)\left(2\sqrt{x}+3\right)}\)

\(=\frac{-10x-7\sqrt{x}+12+18x-8}{\left(3\sqrt{x}-2\right)\left(2\sqrt{x}+3\right)}+\frac{29\sqrt{x}-28}{3\left(3\sqrt{x}-2\right)\left(2\sqrt{x}+3\right)}\)

\(=\frac{8x-7\sqrt{x}+4}{\left(3\sqrt{x}-2\right)\left(2\sqrt{x}+3\right)}+\frac{29\sqrt{x}-28}{3\left(3\sqrt{x}-2\right)\left(2\sqrt{x}+3\right)}\)

\(=\frac{24x-21\sqrt{x}+12}{3\left(3\sqrt{x}-2\right)\left(2\sqrt{x}+3\right)}+\frac{29\sqrt{x}-28}{3\left(3\sqrt{x}-2\right)\left(2\sqrt{x}+3\right)}=\frac{24x+8\sqrt{x}-16}{3\left(3\sqrt{x}-2\right)\left(2\sqrt{x}+3\right)}\)

\(=\frac{8\left(3x+\sqrt{x}-2\right)}{3\left(3\sqrt{x}-2\right)\left(2\sqrt{x}+3\right)}=\frac{8\left(3\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}{3\left(3\sqrt{x}-2\right)\left(2\sqrt{x}+3\right)}=\frac{8\left(\sqrt{x}+1\right)}{3\left(2\sqrt{x}+3\right)}\)

10: \(\frac{2\sqrt{x}-4}{3\sqrt{x}-4}-\frac{2\sqrt{x}+4}{\sqrt{x}-2}+\frac{x+13\sqrt{x}-20}{3x-10\sqrt{x}+8}\)

\(=\frac{\left(2\sqrt{x}-4\right)\left(\sqrt{x}-2\right)-\left(2\sqrt{x}+4\right)\left(3\sqrt{x}-4\right)+x+13\sqrt{x}-20}{\left(3\sqrt{x}-4\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{2x-8\sqrt{x}+8-\left(6x+4\sqrt{x}-16\right)+x+13\sqrt{x}-20}{\left(3\sqrt{x}-4\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{3x+5\sqrt{x}-12-6x-4\sqrt{x}+16}{\left(3\sqrt{x}-4\right)\left(\sqrt{x}-2\right)}=\frac{-3x+\sqrt{x}+4}{\left(3\sqrt{x}-4\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{-3x+4\sqrt{x}-3\sqrt{x}+4}{\left(3\sqrt{x}-4\right)\left(\sqrt{x}-2\right)}=\frac{\left(3\sqrt{x}-4\right)\left(-\sqrt{x}-1\right)}{\left(3\sqrt{x}-4\right)\left(\sqrt{x}-2\right)}=\fr...