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

\(MC=x\left(2-x\right)\left(x+2\right)\)

\(\dfrac{1}{x+2}=\dfrac{x\left(2-x\right)}{x\left(2-x\right)\left(x+2\right)}\);\(\dfrac{8}{2x-x^2}=\dfrac{8\left(x+2\right)}{x\left(2-x\right)\left(x+2\right)}\)

b,

MC : \(x^2-1\)

\(x^2+1=\dfrac{\left(x^2+1\right)\left(x^2-1\right)}{x^2-1}=\dfrac{x^4-1}{x^2-1}\) ; \(\dfrac{x^4}{x^2-1}\)

\(\dfrac{9}{17}\times\dfrac{21}{13}+\dfrac{9}{17}\times\dfrac{5}{13}-\dfrac{9}{17}\times2\)

\(=\dfrac{9}{17}\times\left(\dfrac{21}{13}+\dfrac{5}{13}-2\right)\)

\(=\dfrac{9}{17}\times\left(\dfrac{26}{13}-2\right)=\dfrac{9}{17}\times\left(2-2\right)\)

\(=\dfrac{9}{17}\times0=0\)

= 9/17 x ( 21/13 + 5/13 - 2 )

= 9/17 x 0

= 0

=9/17 x (21/13 + 5/13 - 2)

=9/17 x (26/13 - 2)

=9/17 x (13 - 2)

=9/17 x 11

= 99/17

Tick cho mik nhé!!!

\(\dfrac{-19}{23}\cdot\dfrac{13}{14}+\dfrac{13}{14}\cdot\dfrac{-15}{23}-\dfrac{13}{14}\cdot\dfrac{1}{23}\\ =\dfrac{13}{14}\cdot\left(\dfrac{-19}{23}+\dfrac{-15}{23}-\dfrac{1}{23}\right)\\ =\dfrac{13}{14}\cdot\dfrac{-35}{23}=\dfrac{-65}{46}\)

Áp dụng t/c dtsbn:

\(\dfrac{x-1}{8}=\dfrac{x+1}{12}=\dfrac{x+1-x+1}{12-8}=\dfrac{2}{4}=\dfrac{1}{2}\)

\(\Rightarrow x-1=\dfrac{1}{2}.8=4\Rightarrow x=4+1=5\)

12(x-1)=8(x+1)

12x - 12 =8x + 8

12x - 8x = 8 +12

4x.           = 20

  x.            = 20 :4 

   x.           = 5

a) \(3+\dfrac{5}{2}=\dfrac{6}{2}+\dfrac{5}{2}=\dfrac{11}{2}\)

b) \(\dfrac{2}{8}:\dfrac{4}{8}=\dfrac{2}{8}.\dfrac{8}{4}=\dfrac{2}{4}=\dfrac{1}{2}\)

c) \(\dfrac{13}{5}-2=\dfrac{26}{10}-\dfrac{20}{10}=\dfrac{6}{10}=\dfrac{3}{5}\)

a)\(=\dfrac{6}{2}+\dfrac{5}{2}=\dfrac{11}{2}\)

b)\(=\dfrac{2}{8}\cdot\dfrac{8}{4}=\dfrac{2}{4}=\dfrac{1}{2}\)

c)\(=\dfrac{13}{5}-\dfrac{10}{5}=\dfrac{3}{5}\)

a  \(\dfrac{18}{6}+\dfrac{15}{6}=\dfrac{33}{6}=\dfrac{11}{2}\)

b \(\dfrac{2}{8}\times\dfrac{8}{4}=\dfrac{2}{1}\times\dfrac{1}{4}=\dfrac{2}{4}=\dfrac{1}{2}\)

c \(\dfrac{13}{5}-\dfrac{10}{5}=\dfrac{3}{5}\)

` @Answer`

Để \(B=\dfrac{5}{n-3}\in Z\)

\(\Rightarrow n-3\inƯC\left(5\right)\)

Mà \(ƯC\left(5\right)=\left\{\pm1;\pm5\right\}\)

Ta có : 

`n-3=-1=> n=2`

`n-3=1=>n=4`

`n-3=-5=>n=-2`

`n-3=5=>n=8`

\(\rightarrow n\in\left\{2;4;-2;8\right\}\)

B nguyên thì n-3 là ước của 5

hay n - 3 = {5; 1; -1; -5)

n = {8; 4; 2; 2}

=>x-3=16

hay x=19

\(2^2.\left(x-3\right)=2^6\\ \Rightarrow x-3=16\\ \Rightarrow x=19\)

2²x(x-3)=2⁶

x-3=2⁶:2²

x-3=2^6-2

x-3=2⁴

x-3=16

x=16+3

x=19