\(a,B=\frac{10n}{5n-3}\)

\(\Rightarrow B=\frac{10n-6+6}{5n-3}=2+\frac{6}{5n-3}\)

Để \(B\in Z\Rightarrow5n-3\inƯ\left(6\right)=\left(1;-1;2;-2;3;-3;6;-6\right)\)

\(\Rightarrow5n\in\left(4;2;5;1;6;0;9;-3\right)\)

\(\Rightarrow n\in\left(\frac{4}{5};\frac{2}{5};1;\frac{1}{5};\frac{6}{5};0;\frac{9}{5};-\frac{3}{5}\right)\)

b,\(B=2+\frac{6}{5n-3}\)

Để B đạt GTNN

\(\Rightarrow\frac{6}{5n-3}\)phải có giá trị nhỏ nhất

\(\Rightarrow\frac{6}{5n-3}=-6\Leftrightarrow5n=-1+3=2\Leftrightarrow n=\frac{2}{5}\)

Vậy Min B = 2+(-6)=-4 khi \(n=\frac{2}{5}\)

* Tìm GTNN : 

Ta có : 

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

Để A đạt GTNN thì \(\frac{3}{n-2}\) phải đạt GTNN hay \(n-2< 0\) và đạt GTLN 

\(\Rightarrow\)\(n-2=-1\)

\(\Rightarrow\)\(n=1\)

Suy ra : 

\(A=\frac{n+1}{n-2}=\frac{1+1}{1-2}=\frac{2}{-1}=-2\)

Vậy \(A_{min}=-2\) khi \(n=1\)

Chúc bạn học tốt ~ 

a, bạn sửa lại đề nhé 

b, \(C=\frac{2n+1}{4n+6}=\frac{4n+4}{4n+6}=\frac{4n+6-2}{4n+6}=1-\frac{2}{4n+6}=1-\frac{1}{2n+3}\)

\(\Rightarrow2n+3\inƯ\left(1\right)=\left\{\pm1\right\}\)

\(D=\frac{2n+1}{n-3}=\frac{2\left(n+\frac{1}{2}\right)}{n-3}=\frac{2\left(n-3+\frac{7}{2}\right)}{n-3}\)

\(=\frac{2\left(n-3\right)+7}{n-3}=2+\frac{7}{n-3}\Rightarrow n-3\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)

Gọi ƯCLN(9n+24; 3n+4) là d. Ta có:

9n+24 chia hết cho d

3n+4 chia hết cho d => 9n+12 chia hết cho d

=> 9n+24-(9n+12) chia hết cho d

=> 12 chia hết cho d

=> d thuộc Ư(12)

=> d thuộc {1; -1; 3; -3; 4; -4; 12; -12}

Giả sử ƯCLN(9n+24; 3n+4) khác 1

=> 3n+4 chia hết cho 4

=> 3n+4-4 chia hết cho 4

=> 3n chia hết cho 4

=> nchia hết cho 4

=> n = 4k

=> Để ƯCLN(9n+24; 3n+4) = 1 thì n \(\ne\) 4k

chỉ cần do biểu thức đó có giá trị là số nguyê=> 9n+4 chia hết 3n-2 rồi tìm n thôi

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đợi lát

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a) Để phân số A đạt giá trị nguyên thì 9n + 7 phải chia hết cho 3n + 4 

9n + 7 = 9n + 12 - 5 = 3(3n+4) - 5 

Vì 3(3n+4) chia hết cho 3n + 4 nên 5 chia hết cho 3n + 4 

Hay 3n +4 \(\in\)Ư(5)

3n + 4 = { 1,5,-1,-5}

3n = { -3 ; 1 ; -5 ; -9}

b) Thế vô,cái nào nhỏ nhất thì nhận :v