a) 2.(x-3) - 3.(x-5) = 4.(3-x) - 18

=> 2x - 6 - 3x + 15 = 12 - 4x - 18

=> 2x - 3x + 4x = 12 - 18 + 6 - 15

3x = -15

x = -5

b) ta có: -2x - 11 chia hết cho 3x + 2

=> -6x - 33 chia hết cho 3x + 2

=> -6x - 4 - 29 chia hết cho 3x + 2

-2.(3x+2) - 29 chia hết cho 3x + 2

mà -2.(3x+2) chia hết cho 3x + 2

=> 29 chia hết cho 3x + 2

=>....

bn tự làm tiếp nha!
 

Câu a:

\(\frac{x+5}{x+9}\) = \(\frac{x+4}{x+3}\)

(\(x\) + 5)(\(x+3\)) = (\(x+4\))(\(x+9\))

\(x^2\) + 3\(x\) + 5\(x\) + 15 = \(x^2\) + 9\(x\) + 4\(x\) + 36

\(x^2+3x+5x\) - \(x^2-9x\) - 4\(x\) = 36 - 15

(\(x^2-x^2\)) + (\(3x+5x\) - 9\(x-4x\)) = 21

0 + (8\(x\) - 9\(x\) - 4\(x\)) = 21

-\(x-4x\) = 21

-5\(x\) = 21

\(x\) = 21 : (-5)

\(x\) = - \(\frac{21}{5}\)

Vậy \(x=-\frac{21}{5}\)

b) x-7\(⋮\)x+6

\(\Rightarrow\)x+6-13\(⋮\)x+6

\(\Rightarrow\)13\(⋮\)x+6

\(\Rightarrow\)x+6 \(\in\) Ư(13)

Ta có Ư(13)={\(\pm1;\pm13\)}

nếu x+6=1 thì x=-5

nếu x+6=-1 thì x=-7

nếu x+6=13 thì x=7

nếu x+6=-13 thì x=-19

Vậy x \(\in\) {-5;-7;7;-19}

a) Ta có: \(-2x-11⋮3x+2\)

\(\Rightarrow-3\left(-2x-11\right)⋮3x+2\)

\(\Rightarrow6x+33⋮3x+2\)

\(\Rightarrow\left(6x+4\right)+29⋮3x+2\)

\(\Rightarrow2\left(3x+4\right)+29⋮3x+2\)

\(\Rightarrow29⋮3x+2\)

\(\Rightarrow3x+2\in\left\{1;-1;29;-29\right\}\)

\(\left[\begin{matrix}3x+2=1\\3x+2=-1\\3x+2=29\\3x+2=-29\end{matrix}\right.\Rightarrow\left[\begin{matrix}x=-\frac{1}{3}\\x=-1\\x=9\\x=-\frac{31}{3}\end{matrix}\right.\)

Vậy \(x\in\left\{\frac{-1}{3};-1;9;\frac{-31}{3}\right\}\)

b) \(x-7⋮x+6\)

\(\Rightarrow\left(x+6\right)-13⋮x+6\)

\(\Rightarrow13⋮x+6\)

\(\Rightarrow x+6\in\left\{1;-1;13;-13\right\}\)

\(\left[\begin{matrix}x+6=1\\x+6=-1\\x+6=13\\x+6=-13\end{matrix}\right.\Rightarrow\left[\begin{matrix}x=-5\\x=-7\\x=7\\x=-19\end{matrix}\right.\)

Vậy \(x\in\left\{-5;-7;7;-19\right\}\)

d, ( x+1) nhé. Mình viết nhầm

Trả lời nhanh hộ mình

a)\(\frac{x+11}{x-6}=\frac{x-6+17}{x-6}=\frac{x-6}{x-6}+\frac{17}{x-6}\)

=>x-6\(\in\) Ư(17)

\(a,2x-138=2^3:\left(-3\right)^2\)

\(\Rightarrow2x-138=8:9\)

\(\Rightarrow2x=\frac{8}{9}+138\)

\(\Rightarrow2x=\frac{1250}{9}\)

\(\Rightarrow x=\frac{626}{9}\)

\(10+2x=\left(-4\right)^5:\left(-4\right)^3\)

\(10+2x=-1024:\left(-64\right)\)

\(10+2x=16\)

\(2x=16-10\)

\(2x=6\)

\(x=6:2=3\)

a, 3x - 2 ⋮ x + 3

=> 3x + 9 - 11 ⋮ x + 3

=> 3(x + 3) - 11 ⋮ x + 3

=> 11 ⋮ x + 3

b, x ⋮ 2x + 1

=> 2x ⋮ 2x + 1

=> 2x + 1 - 1 ⋮ 2x + 1

=> 1 ⋮ 2x + 1

c, 3x + 6 ⋮ x + 1

=> 3x + 3 + 3 ⋮ x + 1

=> 3(x + 1) + 3 ⋮ x + 1

=> 3 ⋮ x + 1

d, em không biết làm

câu a,b,c bn Cả Út lm r 

mik làm câu d

\(x^2⋮x-2\)

\(\Rightarrow x\left(x-2\right)+2x⋮x-2\)

\(\Rightarrow2x⋮x-2\)

\(\Rightarrow2\left(x-2\right)+4⋮x-2\)

\(\Rightarrow4⋮x-2\)

\(\Rightarrow x-2\inƯ\left(4\right)=\left\{\pm1;\pm2;\pm4\right\}\)

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

Vậy..............................