Theo bài ra ta có :

(3n+29)⋮(4n+1)=12n+116 ⋮ 12n+12

=12n+12+104 ⋮ 12n+12

Để (3n+29) ⋮ (4n+1)

thì 104 ⋮ 12n+12

hay 12n+12 ∈ Ư₍₁₀₄₎= { 1 ; 104 }

Ta có bảng

vì N∈n

⇒ n không có giá trị thỏa mãn

Vậy không tìm được n

3n + 19 : n - 1

3n - 1 + 20 : n - 1

mà 3n - 1 : n - 1 => 20 : n - 1 => n - 1 thuộc Ư(20) = { 1; 2; 5; 10; 20; -1; -2; -5; -10; -20 }

sau đó tìm n ( như kiểu tìm x ) với các giá trị trên là xong

học tốt ^^

3n+19:n-1

=> n+n+n+19:n-1

=> (n-1)+(n-1)+(n-1)+22:n-1

=> 22:n-1

=> \(n-1\inƯ\left(22\right)\)

mà n > 2

\(\Rightarrow n\in\left\{2;11;22;-2;-11;-22\right\}\)

\(\frac{2n+8}{3n+1}=\frac{3.\left(2n+8\right)}{2.\left(3n+1\right)}=\frac{6n+24}{6n+2}=\frac{6n+2+22}{6n+2}=1+\frac{22}{6n+2}\)

\(n\inℕ\Rightarrow22⋮\left(6n+2\right)\Leftrightarrow6n+2\inƯ\left(22\right)=\left\{1;2;11;22\right\}\)

Nêu 6n+2=1 thì n = -1/6 (loại)

Nếu 6n+2 = 2 thì n = 0

Nếu 6n+2=11 thì n = 3/2 (loại)

Nếu 6n+2=22 thì n = 10/3

Vậy n = 0

Ta có : \(A=\frac{2009.2009+2008}{2009.2009+2009}\)

     \(=1-\frac{1}{2009.2009+2009}\)

        \(B=\frac{2009.2009+2009}{2009.2009+2010}\)

             \(=1-\frac{1}{2009.2009.2010}\)

Mà \(-\frac{1}{2009.2009+2009}< -\frac{1}{2009.2009.2010}\)

=> \(\frac{2009.2009+2008}{2009.2009+2009}< \frac{2009.2009+2009}{2009.2009.2010}\) => A < B

4n - 5 \(⋮\)2n - 4

=> 4n - 8 + 3 \(⋮\)2n - 4

=> 2 . ( 2n - 4 ) + 3 \(⋮\)2n - 4 mà 2 . ( 2n - 4 )  \(⋮\)2n - 4 => 3 \(⋮\)2n - 4

=> 2n - 4 thuộc Ư ( 3 ) = { - 3 ; - 1 ; 1 ; 3 }

Lập bảng tính n ( phần này dễ bạn tự làm nha )

vì 2n-4 chia hết cho 2n-4 suy ra 4n-8 chia hết cho 2n-4 và 4n-5 chia hết cho 2n-4

suy ra (4n-5)-(4n-8) chia hết cho 2n-4

suy ra 3 chia hết cho 2n-4

suy ra 2n-4\(\inƯ\left(3\right)\)

Ta có bảng sau:

NHỚ K CHO MÌNH NHA BẠN!!!!

Good Morning Dear Students!

Today, I am standing here in front of you all as your class teacher and also to deliver a speech on road safety. Now you are no longer small kids who do not know the safety rules while walking on the road. There’s a great saying, “It’s better to be safe than sorry”. However, we tend to forget all this and become carless at times so much so that we risk our lives and put it in danger.

Don’t we keep hearing the news of the count of people who become a victim of road rage or get involved in road accidents? Unfortunately, some die right on the spot and some receive serious injuries that last for the lifetime. Accidents from vehicle have become a big reason behind increased death rates in our country and amidst the time when the government is implementing road safety measures.

Not many of you would know that it is Abu Dhabi which is infamous for holding the highest rate of road deaths in the world. On an average, there are 38 deaths every month because of fatal injuries caused on the road traffic and mainly 0 to 14 year-old children are involved in such cases.

Hence, this establishes the fact that everyone especially pedestrians must remain vigilant while taking the road and must adhere to the safety rules. It is a pedestrian who is chiefly responsible for the accident as it is only when he/she walks carelessly not paying any heed to the traffic signal or do not walk on the designated crosswalk that fatal cases of injuries occur. So I request all of you to remain watchful and never be in a hurry while being on the road. Besides, many people are often seen disrupting the usual flow of traffic, please note that it can also prove very dangerous to one’s lives and therefore should strictly avoid it. Always use zebra crossing in order to walk down the road. Keep your eyes and ears open and listen to the sound of horns if blown around you.

If you are going to travel via public transport and if it’s a bus, then patiently wait for the bus to stop and board it thereafter. wise, if you are going to step out of it, then wait for it to stop properly and make sure that no other vehicle is obstructing your path. Make it a point to carry some reflective material so that the drivers can sense your presence from a distance itself. Never ignore stop signs as when people do that serious road accidents occur.

If you are riding a bicycle on the road, then be even more careful and make sure that your bicycle is in a sound condition with lights and working brakes at their proper places. Secondly, avoid taking bicycle on a busy road and try to use public transport.

However, there is no guarantee that through these preventive measures we will be able to avoid fatal cases of road accidents, but we can definitely avert the danger by remaining vigilant on the road and following all the safety rules. Students, always remember that life doesn’t have a reset button, so never be careless.

Hope all of you will remember my words and in fact would educate others about the importance of road safety rules.

Thank You!

a,

\(\left(n+3\right)⋮\left(n-2\right)\\ \Rightarrow\left(n-2\right)+5⋮\left(n-2\right)\\ \Rightarrow5⋮\left(n-2\right)\\ \Rightarrow\left(n-2\right)\in\left\{{}\begin{matrix}5\\-5\\1\\-1\end{matrix}\right.\\ \Rightarrow n\in\left\{{}\begin{matrix}7\\-3\\4\\2\end{matrix}\right.\)

vì là số tự nhiên nên

\(n\in\left\{{}\begin{matrix}7\\4\\2\end{matrix}\right.\)

b,

\(\text{ ( 2n + 9 ) ⋮ ( n - 3 )}\\ \Rightarrow2\left(n-3\right)+15⋮\left(n-3\right)\\ \Rightarrow15⋮\left(n-3\right)\\ \Rightarrow\left(n-3\right)\inƯ\left(15\right)=\left\{15;5;3;1;-1;-3;-5;-15\right\}\\ \Rightarrow n\in\left\{18;8;6;4;2;0;-2;-13\right\}\)

vì n là số tự nhiên nên:

\(n\in\left\{18;8;6;4;2;0\right\}\)