\(\dfrac{2n+1}{n-1}=\dfrac{2n-2+3}{n-1}=\dfrac{2n-2}{n-1}+\dfrac{3}{n-1}=2+\dfrac{3}{n-1}\)

\(\Rightarrow3⋮n-1\Rightarrow n-1\inƯ\left(3\right)\)

\(Ư\left(3\right)=\left\{\pm1;\pm3\right\}\)

Xét ước

\(n^2+1⋮n+2\)

\(\Rightarrow n^2+2n-2n+1⋮n+2\)

\(\Rightarrow n^2+2n-2n-4+5⋮n+2\)

\(\Rightarrow n\left(n+2\right)-2\left(n+2\right)+5⋮n+2\)

\(\Rightarrow\left(n-2\right)\left(n+2\right)+5⋮n+2\)

\(\Rightarrow5⋮n+2\)

\(\Rightarrow n+2\inƯ\left(5\right)\)

\(Ư\left(5\right)=\left\{\pm1;\pm5\right\}\)

Xét ước

\(\dfrac{n^2-3n+2}{n+1}\)

\(\Rightarrow n^2-3n+2⋮n+1\)

\(\Rightarrow n^2+n-4n+2⋮n+1\)

\(\Rightarrow n^2+n-4n-4+6⋮n+1\)

\(\Rightarrow n\left(n+1\right)-4\left(n+1\right)+6⋮n+1\)

\(\Rightarrow\left(n-4\right)\left(n+1\right)+6⋮n+1\)

\(\Rightarrow6⋮n+1\Rightarrow n+1\inƯ\left(6\right)\)

\(Ư\left(6\right)=\left\{\pm1;\pm2;\pm3;\pm6\right\}\)

Xét ước

\(A=\dfrac{6n+3-2}{2n+1}=3-\dfrac{2}{2n+1}\)

Để A max thì 2/2n+1 min

mà n nguyên

nên 2n+1=-1

=>2n=-2

=>n=-1

a, \(A=\dfrac{5n-4-4n+5}{n-3}=\dfrac{n+1}{n-3}=\dfrac{n-3+4}{n-3}=1+\dfrac{4}{n-3}\Rightarrow n-3\inƯ\left(4\right)=\left\{\pm1;\pm2;\pm4\right\}\)

a.\(A=\dfrac{2n+1}{n-3}+\dfrac{3n-5}{n-3}-\dfrac{4n-5}{n-3}\)

\(A=\dfrac{2n+1+3n-5-4n+5}{n-3}\)

\(A=\dfrac{n+1}{n-3}\)

\(A=\dfrac{n-3}{n-3}+\dfrac{4}{n-3}\)

\(A=1+\dfrac{4}{n-3}\)

Để A nguyên thì \(\dfrac{4}{n-3}\in Z\) hay \(n-3\in U\left(4\right)=\left\{\pm1;\pm2;\pm4\right\}\)

n-3=1 --> n=4

n-3=-1 --> n=2

n-3=2 --> n=5

n-3=-2 --> n=1

n-3=4 --> n=7

n-3=-4 --> n=-1

Vậy \(n=\left\{4;2;5;7;1;-1\right\}\) thì A nhận giá trị nguyên

b.hemm bt lèm:vv

cc

\(a)\,\,A=\dfrac{13}{21} \Leftrightarrow \dfrac{2n+3}{4n+1}=\dfrac{13}{21} \\ \Leftrightarrow 21(2n+3)=13(4n+1)\\\Leftrightarrow 42n+63=52n+13\\\Leftrightarrow 42n-52n=13-63 \\\Leftrightarrow -10n=-50\\\Leftrightarrow n=(-50):(-10)\\\Leftrightarrow n=5\)

1.a) để A là số hữu tỉ thì 2n+3 nguyên và n - 1 khác 0

từ hai điều kiện trên suy ra n nguyên và n khác 1

b) để A nguyên thì 2n+3 ⋮ n - 1

⇒ 2(n - 1) +5 ⋮ n - 1

⇒ 5 ⋮ n - 1

⇒n ∈ {-4; 0; 2; 6}

2. x < y ⇔ \(\dfrac{a}{n}< \dfrac{b}{n}\)

\(\Rightarrow\dfrac{2a}{2n}< \dfrac{a+b}{2n}< \dfrac{2b}{2n}\Leftrightarrow x< z< y\)

BÀi 1

Để A \(\in\) Z

=>\(\left(n+2\right)⋮\left(n-5\right)\)

=>\([\left(n-5\right)+7]⋮\left(n-5\right)\)

=>\(7⋮\left(n-5\right)\)

=>\(n-5\in\left\{1;7;-1;-7\right\}\)

=>\(n\in\left\{6;13;4;-2\right\}\)

Vậy \(n\in\left\{6;13;4;-2\right\}\)

Giúp mk nha

Arigatou gozaimasu!

Để phân số \(A=\dfrac{5n+7}{2n+1}\in Z\) thì :

\(5n+7⋮2n+1\)

Mà \(2n+1⋮2n+1\)

\(\Leftrightarrow\left\{{}\begin{matrix}10n+14⋮2n+1\\10n+5⋮2n+1\end{matrix}\right.\)

\(\Leftrightarrow9⋮2n+1\)

Vì \(n\in Z\Leftrightarrow2n+1\in Z;2n+1\inƯ\left(9\right)\)

Xét ước là ok!

Để phân số \(A=\dfrac{5n+7}{2n+1}\in Z\) thì : \(5n+7⋮2n+1\)

Mà \(2n+1⋮2n+1\)

\(\Leftrightarrow\left\{{}\begin{matrix}10n+14⋮2n+1\\10n+5⋮2n+1\end{matrix}\right.\Leftrightarrow9⋮2n+1\)

Vì \(n\in Z\Leftrightarrow2n+1\in Z;2n+1\inƯ\left(9\right)\)

Xét ước của 9

Vậy .............