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

mà \(n\inℤ\)nên \(3-2n\inƯ\left(5\right)=\left\{-5,-1,1,5\right\}\)

\(\Leftrightarrow n\in\left\{4,2,1,-1\right\}\).

hello

a) Để A là phân số thì \(n-1\ne0\)

hay \(n\ne1\)

Vậy: Để A là phân số thì \(n\ne1\)

b) Để A là số nguyên thì \(4n+3⋮n-1\)

\(\Leftrightarrow4n-4+7⋮n-1\)

mà \(4n-4⋮n-1\)

nên \(7⋮n-1\)

\(\Leftrightarrow n-1\inƯ\left(7\right)\)

\(\Leftrightarrow n-1\in\left\{1;-1;7;-7\right\}\)

hay \(n\in\left\{2;0;8;-6\right\}\)

Kết hợp ĐKXĐ, ta được: \(n\in\left\{2;0;8;-6\right\}\)

Vậy: Để A là số nguyên thì \(n\in\left\{2;0;8;-6\right\}\)

a: Để Q là phân số thì n+5<>0

hay n<>-5

b: Để Q là số nguyên thì \(4n⋮n+5\)

\(\Leftrightarrow n+5\in\left\{1;-1;2;-2;4;-4;5;-5;10;-10;20;-20\right\}\)

hay \(n\in\left\{-4;-6;-3;-7;-1;-9;0;-10;5;-15;15;-25\right\}\)

như đb

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

Để A nguyên thì \(\frac{-5}{2n+3}\) phải nguyên

=> \(2n+3\inƯ\left(-5\right)=\left\{1;-1;5;-5\right\}\)

=> \(n\in\left\{-1;-2;1;-4\right\}\)

a,4n+>2n+3nên n =5,6

b,7,8

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

Để \(2-\frac{5}{2n+3}\) là số nguyên <=> \(\frac{5}{2n+3}\) là số nguyên

=> 2n + 3 thuộc Ư(5) = { - 5; - 1; 1; 5 }

=> 2n + 3 = { - 5; - 1; 1; 5 }

=> n = { - 4; - 2; - 1 ; 1 }

a) Ta có:

\(\frac{4n+1}{2n+3}\inℤ\)

\(\Rightarrow\frac{4n-2+3}{2n+3}\inℤ\)

\(\Rightarrow\frac{2n+2n+3-2}{2n+3}\inℤ\)

\(\Rightarrow\frac{2n+3}{2n+3}+\frac{2n-2}{2n+3}\inℤ\)

\(\Rightarrow1+\frac{2n-2}{2n+3}\inℤ\Leftrightarrow\frac{2n-2}{2n+3}\inℤ\)

\(\Rightarrow\frac{2n+3-5}{2n+3}\inℤ\)

\(\Rightarrow1+\frac{-5}{2n+3}\inℤ\Leftrightarrow\frac{-5}{2n+3}\inℤ\)

\(\Rightarrow\left(2n+3\right)\in B\left(-5\right)=\left\{1;-1;5;-5\right\}\)

\(\Rightarrow\left(2n+3\right)=\left\{1;-1;5;-5\right\}\)

\(\Rightarrow2n=\left\{-2;-4;2;-8\right\}\)

\(\Rightarrow n=\left\{-1;-2;1;-4\right\}\)

Để A là số nguyên thì

4n+1\(^._:\)2n+3

=>4n+6-5\(^._:\)2n+3

Vì 4n+6\(^._:\)2n+3

=>5\(^._:\)2n+3

=>2n+3\(\in\)Ư(5)={1;-1;5;-5}

Ta có bảng sau:

KL: n\(\in\){-1;-2;1;-4}

I don't now

mik ko biết 

sorry 

......................

1)\(4n+3⋮n-2\)

\(\Leftrightarrow4n+3=4\left(n-2\right)+11\)

\(\Rightarrow4\left(n-2\right)⋮n-2\)\(\Rightarrow n-2⋮n-2\)

\(\Rightarrow11⋮n-2\)

\(\Rightarrow n-2\in\left\{\pm1;\pm11\right\}\)

\(\Rightarrow n\in\left\{3;1;13;-9\right\}\)

2)\(xy+5x+y+10=0\)

\(\Leftrightarrow x\left(y+5\right)+y+5+5=0\)

\(\Leftrightarrow x\left(y+5\right)+\left(y+5\right)=-5\)

\(\Leftrightarrow\left(x+1\right).\left(y+5\right)=-5\)

3)