a: \(=\dfrac{3}{11}+\dfrac{18}{66}=\dfrac{18}{66}+\dfrac{18}{66}=\dfrac{36}{66}=\dfrac{6}{11}\)

b: \(=\dfrac{2}{9}-\dfrac{5}{12}+\dfrac{3}{4}\)

\(=\dfrac{8}{36}-\dfrac{15}{36}+\dfrac{27}{36}=\dfrac{20}{36}=\dfrac{5}{9}\)

c: \(=\dfrac{3\cdot7-5}{35}\cdot\dfrac{-40-30}{16}\)

\(=\dfrac{16}{35}\cdot\dfrac{-70}{16}=-2\)

d: \(=\dfrac{1}{5}\cdot\dfrac{2-7}{4}-\dfrac{3}{4}\cdot\dfrac{4-11}{12}\)

\(=\dfrac{1}{5}\cdot\dfrac{-5}{4}-\dfrac{3}{4}\cdot\dfrac{-7}{12}\)

\(=\dfrac{-1}{4}+\dfrac{21}{48}=\dfrac{-12+21}{48}=\dfrac{9}{48}=\dfrac{3}{16}\)

a: \(\Leftrightarrow x^2=16\)

hay \(x\in\left\{4;-4\right\}\)

b: \(\Leftrightarrow\dfrac{20}{6-5x}=\dfrac{5}{14}\)

=>6-5x=56

=>5x=-50

hay x=-10

c: =>7/17=x/119=-35/y

=>x=49; y=-85

d: =>x/27=1/9+1/9=2/9

hay x=6

\(a,\dfrac{x}{-2}=\dfrac{-8}{x}\)

\(\Leftrightarrow x^2=16\Rightarrow\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\)

\(b,\dfrac{5}{14}=\dfrac{20}{6-5x}\)

\(\Leftrightarrow30-25x=280\)

\(\Leftrightarrow25x=30-280=-250\)

\(\Leftrightarrow x=-10\)

\(c,\dfrac{7}{17}=\dfrac{x}{119}=\dfrac{-35}{y}\)

\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{119.7}{17}=49\\y=\dfrac{-35.17}{7}=-85\end{matrix}\right.\)

\(d,\dfrac{x}{27}+\dfrac{-3}{27}=\dfrac{1}{9}\)

\(\dfrac{x-3}{27}=\dfrac{1}{9}\)

\(9x-27=27\)

\(9x=54\Rightarrow x=6\)

a)\(\dfrac{x}{-2}=-\dfrac{8}{x}\)

\(\Rightarrow x^2=16\)

\(\Rightarrow x=-4\) hoặc x=4

b)\(-\dfrac{5}{-14}=\dfrac{20}{6-5x}\)

\(\Rightarrow-5\left(6-5x\right)=-280\)

\(-30+25x=-280\)

25x=-250

x=-10

c)\(\dfrac{7}{17}=\dfrac{x}{119}=-\dfrac{35}{y}\)

\(\Rightarrow\dfrac{x}{119}=\dfrac{7}{17}\Rightarrow x=49\)

     \(-\dfrac{35}{y}=\dfrac{7}{17}\Rightarrow y=-85\)

d)\(\dfrac{x}{27}+\dfrac{-3}{27}=\dfrac{1}{9}\)

\(\dfrac{x-3}{27}=\dfrac{1}{9}\)

\(x-3=3\)

x=6

e: \(=\dfrac{-5}{4}:\dfrac{-5}{8}+\dfrac{3}{2}\cdot\dfrac{-1}{2}=\dfrac{5}{4}\cdot\dfrac{8}{5}-\dfrac{3}{4}=2-\dfrac{3}{4}=\dfrac{5}{4}\)

f: \(=\dfrac{15}{7}\cdot\left(-7\right)\cdot\dfrac{-1}{10}=15\cdot\dfrac{1}{10}=\dfrac{3}{2}\)

g: \(=\dfrac{7}{10}\cdot\dfrac{-8}{7}:\dfrac{8}{15}-\dfrac{1}{3}\cdot\dfrac{1}{4}=\dfrac{-4}{5}\cdot\dfrac{15}{8}-\dfrac{1}{12}=\dfrac{-3}{2}-\dfrac{1}{12}=\dfrac{-19}{12}\)

Lời giải:
a.

$\frac{x}{-2}=\frac{-8}{x}$

$\Rightarrow x^2=(-2)(-8)=16=4^2=(-4)^2$

$\Rightarrow x=4$ hoặc $x=-4$

b.

$\frac{-5}{-14}=\frac{20}{6-5x}$

$\frac{5}{14}=\frac{20}{6-5x}$

$\Rightarrow 6-5x=20.14:5=56$

$x=-10$

c: 7/17=x/119=-35/y

\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{119\cdot7}{17}=49\\y=\dfrac{-35\cdot17}{7}=-85\end{matrix}\right.\)

d: =>x/27-1/9=1/9

=>x/27=2/9

=>x=6

\(a,\dfrac{-1}{3}-x=\dfrac{1}{5}-\dfrac{1}{-2}\\ \Rightarrow\dfrac{-1}{3}-x=\dfrac{7}{10}\\ \Rightarrow x=-\dfrac{31}{30}\\ b,\dfrac{3}{7}:x=\dfrac{1}{4}-\dfrac{3}{2}\\ \Rightarrow\dfrac{3}{7}:x=-\dfrac{5}{4}\\ \Rightarrow x=-\dfrac{12}{35}\\ c,\dfrac{4}{9}.x+\dfrac{1}{3}=\dfrac{5}{6}\\ \Rightarrow\dfrac{4}{9}.x=\dfrac{1}{2}\\ \Rightarrow x=\dfrac{9}{8}\\ d,\dfrac{2}{5}+\dfrac{3}{5}.x=\dfrac{14}{15}\\ \Rightarrow\dfrac{3}{5}.x=\dfrac{8}{15}\\ \Rightarrow x=\dfrac{8}{9}\)

a: \(=\left(\dfrac{2}{5}-\dfrac{2}{5}\right)+\left(\dfrac{5}{4}+\dfrac{5}{4}\right)-\dfrac{5}{2}=\dfrac{10}{4}-\dfrac{5}{2}=0\)

b: \(=\left(-\dfrac{2}{11}-\dfrac{9}{11}\right)+\left(\dfrac{6}{7}+\dfrac{1}{7}\right)+\left(\dfrac{1}{2}+\dfrac{1}{3}\right)=\dfrac{5}{6}\)

c: \(=\dfrac{7}{19}\left(\dfrac{5}{13}+\dfrac{8}{13}-3\right)=\dfrac{7}{19}\cdot\left(-2\right)=-\dfrac{14}{19}\)

d: \(=\dfrac{12}{11}+\dfrac{9}{22}\left(\dfrac{7}{15}+\dfrac{8}{15}\right)=\dfrac{12}{11}+\dfrac{9}{22}=\dfrac{24+9}{22}=\dfrac{33}{22}=\dfrac{3}{2}\)

b) Gọi 4 số tự nhiên liên tiếp có dạng : p , p + 1 , p + 2 , p +3

Tổng 4 số là :

p + p + 1 + p + 2 + p + 3 = p + p + p + p + ( 1 + 2 + 3 ) = p . ( 1 + 1 + 1 + 1 ) + 6 = 4p + 6 không chia hết cho 4

Vậy tổng 4 số tự nhiên liên tiếp không chia hết cho 4

a) Gọi 3 số tự nhiên liên tiếp có dang : p , p + 1 , p + 2

Tổng các số là : 

p + p + 1 + p + 2 = p + p + p + ( 1 + 2 ) = p + p + p + 3 = p . ( 1 + 1 + 1 ) + 3 = 3p + 3 chia hết cho 3

Vậy tổng 3 số tự nhiên liến tiếp chia hết cho 3