some->any

`-2/4 = 1/(x-1)`

`=> -2(x-1)=4.1`

`=> -2(x-1)=4`

`=> x-1=4:(-2)`

`=> x-1=-2`

`=>x=-2+1`

`=>x=-1`

(n+3) ⋮ (2n-1)

=> 2.(n+3)⋮2n-1

=> 2n+6 ⋮ 2n-1

=> (2n-1)+7⋮2n-1

mà 2n-1⋮2n-1

=> 7⋮2n-1

=>2n-1∈Ư(7)={1;7}

=>2n∈{2;8}

=>n∈{1;4}

Vậy n∈{1;4}

\(=\dfrac{1}{3}:\dfrac{7\cdot\left(5+3\right)}{18\cdot\left(53-11\right)}\) 

\(=\dfrac{1}{3}:\dfrac{7\cdot8}{18\cdot42}\) 

\(=\dfrac{1}{3}:\dfrac{7\cdot2\cdot2\cdot2}{3\cdot3\cdot2\cdot2\cdot3\cdot7}\)

\(=\dfrac{1}{3}:\dfrac{2}{3\cdot3\cdot3}\)

\(=\dfrac{1}{3}\cdot\dfrac{27}{2}\)

\(=\dfrac{9}{2}\)

\(\left(-12\right).65+7.12-8.\left(-12\right)\)

\(=-12\left(65-7-8\right)\)

\(=-12.50\)

\(=-600\)

\(2^{x+3}.2=2^2.3+52\)

\(=>2^{x+3}.2=64\)

\(=>2^{x+3}=64:2\)

\(=>2^{x+3}=32\)

\(=>2^{x+3}=2^5\)

=>x+3=5

=>x=5-3

=>x=2

Vậy ...........

 2^{x + 3} . 2 = 2² . 3 + 52

 2^{x + 3} . 2 = 4 . 3 + 52

 2^{x + 3} . 2 = 12 + 52

 2^{x + 3} . 2 = 64

     2^{x + 3}  = 64 : 2

     2^{x + 3}  = 32

     2^{x + 3} = 2⁵

     x + 3 = 5

           x = 5 - 3

           x = 2

Vậy x = 2

`x/2=2/x`

`=>x.x=2.2`

`=>x^2=4`

`=>x=+-2`

\(\dfrac{-1}{4}< \dfrac{x}{24}< \dfrac{-1}{6}\\ \dfrac{-6}{24}< \dfrac{x}{24}< \dfrac{-4}{24}\\ \Rightarrow x=-5\)

\(\dfrac{-1}{4}< \dfrac{x}{24}< \dfrac{-1}{6}\)
\(\Rightarrow\dfrac{-6}{24}< \dfrac{x}{24}< \dfrac{-4}{24}\)
\(\Rightarrow-6< x< -4\)
\(\Rightarrow x=-5\)

`(-1)/4 < x/24 < (-1)/6`

`(-6)/24 < x/24 < (-4)/24`

`->x=-5`

Lời giải:

Vì $a,b$ là số tự nhiên nên $2a+1,b-2$ là số nguyên

$(2a+1)(b-2)=12$ nên $2a+1$ là ước của $12$
Mà $2a+1$ là số tự nhiên lẻ nên $2a+1\in\left\{1;3\right\}$

Nếu $2a+1=1$ thì $b-2=12:1=12$

$\Rightarrow a=0; b=14$ (thỏa mãn)

Nếu $2a+1=3$ thì $b-2=12:3=4$

$\Rightarrow a=1; b=6$ (thỏa mãn)