Bài 4: 

a: \(\Leftrightarrow n-1\in\left\{1;-1;5;-5\right\}\)

hay \(n\in\left\{2;0;6;-4\right\}\)

senpai đang viết j vậy

Bài 1:

a: \(\left\lbrack77-\left(-23\right)\right\rbrack\cdot54-\left\lbrack135+\left(-35\right)\right\rbrack\cdot\left(-6\right)\)

\(=\left(77+23\right)\cdot54+6\cdot100\)

\(=100\cdot\left(54+6\right)=60\cdot100=6000\)

b: \(99\left(123-56\right)+\left(-99\right)\left(-66+123\right)\)

=99(123-56+66-123)

=99*10=990

c: \(547-547\cdot\left(-103\right)+4\cdot\left(-547\right)\)

\(=547+547\cdot103-547\cdot4\)

\(=547\left(1+103-4\right)=547\cdot100=54700\)

d: \(\left(-76\right)\cdot2+76\cdot\left(-9\right)+76\)

\(=76\left(-2-9+1\right)\)

\(=76\cdot\left(-10\right)=-760\)

Bài 4:

a: n-1∈Ư(n+4)

=>n+4⋮n-1

=>n-1+5⋮n-1

=>5⋮n-1

=>n-1∈{1;-1;5;-5}

=>n∈{2;0;6;-4}

b: 3n+7∈B(n+1)

=>3n+7⋮n+1

=>3n+3+4⋮n+1

=>4⋮n+1

=>n+1∈{1;-1;2;-2;4;-4}

=>n∈{0;-2;1;-3;3;-5}

c: 4n+3⋮n+2

=>4n+8-5⋮n+2

=>-5⋮n+2

=>n+2∈{1;-1;5;-5}

=>n∈{-1;-3;3;-7}

d: \(n^2+3n-2\) ⋮n+2

=>\(n^2+2n+n+2-4\) ⋮n+2

=>-4⋮n+2

=>n+2∈{1;-1;2;-2;4;-4}

=>n∈{-1;-3;0;-4;2;-6}

Bài 9:
\(a,\left(2n+1\right)⋮\left(n-1\right)\\ \Rightarrow\left[\left(2n-2\right)+3\right]⋮\left(n-1\right)\\ \Rightarrow\left[2\left(n-1\right)+3\right]⋮\left(n-1\right)\)

Mà \(2\left(n-1\right)⋮\left(n-1\right)\Rightarrow3⋮\left(n-1\right)\Rightarrow n-1\inƯ\left(3\right)=\left\{-3;-1;1;3\right\}\)

Ta có bảng:

Vậy \(n\in\left\{0;2;4\right\}\)

b, c, d bạn làm tương tự nhé

Bài 10:

a: Gọi a=UCLN(n+1;2n+3)

\(\Leftrightarrow2n+3-2\left(n+1\right)⋮a\)

\(\Leftrightarrow1⋮a\)

=>a=1

Vậy: n+1/2n+3 là phân số tối giản

b: Gọi a=UCLN(3n+2;5n+3)

\(\Leftrightarrow5\left(3n+2\right)-3\left(5n+3\right)⋮a\)

\(\Leftrightarrow1⋮a\)

=>a=1

Vậy: 3n+2/5n+3 là phân số tối giản

c: 

hay 

d: 

hay 

a: 

hay 

b: \(\Leftrightarrow n+1\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(n\in\left\{0;-2;1;-3;3;-5\right\}\)

c: \(\Leftrightarrow n+2\in\left\{1;-1;5;-5\right\}\)

hay \(n\in\left\{-1;-3;3;-7\right\}\)

d: \(\Leftrightarrow n+2\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(n\in\left\{-1;-3;0;-4;2;-6\right\}\)

a: \(\Leftrightarrow n-1\in\left\{1;-1;5;-5\right\}\)

hay \(n\in\left\{2;0;6;-4\right\}\)

a: =100x54-100x(-6)

=100x60

=6000

b: =99(123-56+66-123)=990

c: =547x(1+103-4)=54700

d: =-76x10=-760

b: \(\Leftrightarrow n+1\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(n\in\left\{0;-2;1;-3;3;-5\right\}\)

c: \(\Leftrightarrow n+2\in\left\{1;-1;5;-5\right\}\)

hay \(n\in\left\{-1;-3;3;-7\right\}\)

d: \(\Leftrightarrow n+2\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(n\in\left\{-1;-3;0;-4;2;-6\right\}\)

a: \(\Leftrightarrow n-1\in\left\{1;-1;5;-5\right\}\)

hay \(n\in\left\{2;0;6;-4\right\}\)

b: \(\Leftrightarrow n+1\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(n\in\left\{0;-2;1;-3;3;-5\right\}\)

c: \(\Leftrightarrow n+2\in\left\{1;-1;5;-5\right\}\)

hay \(n\in\left\{-1;-3;3;-7\right\}\)

d: \(\Leftrightarrow n+2\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(n\in\left\{-1;-3;0;-4;2;-6\right\}\)

a: \(\Leftrightarrow n-1\in\left\{1;-1;5;-5\right\}\)

hay \(n\in\left\{2;0;6;-4\right\}\)

b: \(\Leftrightarrow n+1\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(n\in\left\{0;-2;1;-3;3;-5\right\}\)

c: \(\Leftrightarrow n+2\in\left\{1;-1;5;-5\right\}\)

hay \(n\in\left\{-1;-3;3;-7\right\}\)

d: \(\Leftrightarrow n+2\in\left\{1;-1;2;-2;4;-4\right\}\)

hay \(n\in\left\{-1;-3;0;-4;2;-6\right\}\)

a: \(\Leftrightarrow n-1\in\left\{1;-1;5;-5\right\}\)

hay \(n\in\left\{2;0;6;-4\right\}\)

a: \(-\dfrac{6}{13}=-\dfrac{12}{26}=\dfrac{-18}{39}=-\dfrac{24}{52}=\dfrac{-30}{65}=\dfrac{-36}{78}=\dfrac{-42}{91}\)

b: \(\dfrac{15}{-7}=\dfrac{-15}{7}=\dfrac{-30}{14}=\dfrac{-45}{21}=\dfrac{-60}{28}=\dfrac{-75}{35}=-\dfrac{90}{42}\)