\(\dfrac{\left(\dfrac{5}{30}+\dfrac{3}{30}+\dfrac{2}{30}\right):\left(\dfrac{5}{30}+\dfrac{3}{30}-\dfrac{2}{30}\right)}{\left(\dfrac{30}{60}-\dfrac{20}{60}+\dfrac{15}{60}-\dfrac{12}{60}\right):\left(\dfrac{3}{12}-\dfrac{2}{12}\right)}=\dfrac{\dfrac{1}{3}:\dfrac{1}{5}}{\dfrac{13}{60}:\dfrac{1}{12}}=\dfrac{\dfrac{1}{3}\times5}{\dfrac{13}{60}\times12}=\dfrac{\dfrac{5}{3}}{\dfrac{13}{5}}=\dfrac{25}{39}\)

=\(\dfrac{\dfrac{1}{3}:\dfrac{1}{5}}{\dfrac{13}{60}:\dfrac{1}{12}}=\dfrac{\dfrac{5}{3}}{\dfrac{13}{5}}=\dfrac{25}{39}\)

25/39

d: \(\left(2^2:\dfrac{4}{3}-\dfrac{1}{2}\right)\cdot\dfrac{6}{5}-17\)

\(=\left(4\cdot\dfrac{3}{4}-\dfrac{1}{2}\right)\cdot\dfrac{6}{5}-17\)

\(=\left(3-\dfrac{1}{2}\right)\cdot\dfrac{6}{5}-17\)

\(=\dfrac{5}{6}\cdot\dfrac{6}{5}-17=1-17=-16\)

h: \(\dfrac{\left(-1\right)^3}{15}+\left(-\dfrac{2}{3}\right)^2:2\dfrac{2}{3}-\left|-\dfrac{5}{6}\right|\)

\(=-\dfrac{1}{15}+\dfrac{-8}{27}:\dfrac{8}{3}-\dfrac{5}{6}\)

\(=-\dfrac{1}{15}-\dfrac{1}{9}-\dfrac{5}{6}\)

\(=\dfrac{-6-10-75}{90}=\dfrac{-91}{90}\)

k: \(\dfrac{2\cdot6^9-2^5\cdot18^4}{2^2\cdot6^8}\)
\(=\dfrac{2^{10}\cdot3^9-2^5\cdot2^4\cdot3^8}{2^2\cdot2^8\cdot3^8}\)

\(=\dfrac{2^{10}\cdot3^9-2^9\cdot3^8}{2^{10}\cdot3^8}=\dfrac{2^9\cdot3^8\left(2\cdot3-1\right)}{2^{10}\cdot3^8}\)

\(=\dfrac{5}{2}\)

n: \(3-\left(-\dfrac{7}{8}\right)^0+\left(\dfrac{1}{2}\right)^3\cdot16\)

\(=3-1+\dfrac{1}{8}\cdot16\)

=2+2

=4

a) \(\dfrac{-4}{6}\)

b) \(\dfrac{1}{3}\)-\(\dfrac{20}{60}\)

= 0 

c) \(-20^2\)+(\(-50^3\))

= -400 + (-125000)

=-125400

d) \(\dfrac{-2}{7}\)+\(\dfrac{15}{35}\)

= \(\dfrac{-10}{35}\)+\(\dfrac{15}{35}\)

= \(\dfrac{5}{35}\)=\(\dfrac{1}{7}\)

Nhớ tick cho mk nha

a) \(\dfrac{-5}{6}+\dfrac{1}{6}=\dfrac{-5+1}{6}=\dfrac{-4}{6}=\dfrac{-2}{3}\)

b) \(\dfrac{1}{3}-\dfrac{5}{4}\cdot\dfrac{4}{15}=\dfrac{1}{3}-\dfrac{1}{3}=0\)

1/ ĐKXĐ : \(x\ne1\)

\(\dfrac{7x-3}{x-1}=\dfrac{2}{3}\)

\(\Leftrightarrow21x-9=2x-2\)

\(\Leftrightarrow19x=7\Leftrightarrow x=\dfrac{7}{19}\left(tm\right)\)

Vậy...

b/ \(\dfrac{2\left(3-7x\right)}{1+x}=\dfrac{1}{2}\) ĐKXĐ : \(x\ne-1\)

\(\Leftrightarrow12-28x=1+x\)

\(\Leftrightarrow11=29x\Leftrightarrow x=\dfrac{11}{29}\) \(\left(tm\right)\)

Vậy....

c/ ĐKXĐ : \(x\ne0\)

\(\dfrac{x^2-6}{x}=x+\dfrac{3}{2}\)

\(\Leftrightarrow\dfrac{x^2-6}{x}=\dfrac{2x+3}{2}\)

\(\Leftrightarrow2x^2-12=2x^2+3x\)

\(\Leftrightarrow3x=-12\Leftrightarrow x=-4\) \(\left(tm\right)\)

Vậy...

4/ ĐKXĐ : \(x\ne-\dfrac{2}{3}\)

\(\dfrac{5}{3x+2}=2x-1\)

\(\Leftrightarrow\left(2x-1\right)\left(3x+2\right)=5\)

\(\Leftrightarrow6x^2+4x-3x-2=5\)

\(\Leftrightarrow6x^2+x-7=0\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{7}{6}\\x=1\end{matrix}\right.\)

Vậy....

5,6 Tương tự nhé !

1)ĐKXĐ: \(x\ne1\)

Ta có: \(\dfrac{7x-3}{x-1}=\dfrac{2}{3}\)

\(\Leftrightarrow3\left(7x-3\right)=2\left(x-1\right)\)

\(\Leftrightarrow21x-9=2x-2\)

\(\Leftrightarrow21x-9-2x+2=0\)

\(\Leftrightarrow19x-7=0\)

\(\Leftrightarrow19x=7\)

\(\Leftrightarrow x=\dfrac{7}{19}\)(nhận)

Vậy: \(S=\left\{\dfrac{7}{19}\right\}\)

2) ĐKXĐ: \(x\ne-1\)

Ta có: \(\dfrac{2\left(3-7x\right)}{1+x}=\dfrac{1}{2}\)

\(\Leftrightarrow4\left(3-7x\right)=x+1\)

\(\Leftrightarrow12-28x-x-1=0\)

\(\Leftrightarrow-29x+11=0\)

\(\Leftrightarrow-29x=-11\)

\(\Leftrightarrow x=\dfrac{11}{29}\)

Vậy: \(S=\left\{\dfrac{11}{29}\right\}\)

3) ĐKXĐ: \(x\ne0\)

Ta có: \(\dfrac{x^2-6}{x}=x+\dfrac{3}{2}\)

\(\Leftrightarrow\dfrac{x^2-6}{x}=\dfrac{2x+3}{2}\)

\(\Leftrightarrow2\left(x^2-6\right)=x\left(2x+3\right)\)

\(\Leftrightarrow2x^2-12=2x^2+6x\)

\(\Leftrightarrow2x^2-12-2x^2-6x=0\)

\(\Leftrightarrow-6x-12=0\)

\(\Leftrightarrow-6x=12\)

\(\Leftrightarrow x=-2\)

Vậy: S={-2}

a: \(\Leftrightarrow\dfrac{-13}{3}\cdot\dfrac{1}{3}< =x< =\dfrac{-2}{5}\cdot\dfrac{-11}{12}\)

=>-13/9<=x<=22/60

mà x là số nguyên

nên \(x\in\left\{-1;0\right\}\)

b: \(\Leftrightarrow\dfrac{-22}{5}\cdot\dfrac{10}{3}< =x< =\dfrac{-13}{5}:\dfrac{7}{5}\)

=>-44/3<=x<=-13/7

mà x là số nguyên

nên \(x\in\left\{-14;-13;...;-2\right\}\)

2: \(=\dfrac{203}{60}\cdot\dfrac{81}{1225}=\dfrac{783}{3500}\)

a) \(\left(\dfrac{2}{3}-\dfrac{1}{2}-\dfrac{1}{3}\right)\cdot\left(1-\dfrac{1}{4}-\dfrac{1}{7}\right)\)

\(=-\dfrac{1}{6}\cdot\dfrac{17}{28}\)

\(=-\dfrac{17}{168}\)

b)  \(\left(\dfrac{15}{21}\div\dfrac{5}{7}\right)\div\left(\dfrac{6}{5}\div2\right)\)

\(=1\div\dfrac{3}{5}\)

\(=\dfrac{5}{3}\)

(2/3 - 1/2 - 1/3) . (1-1/4 - 1/7)

= -1/6 . 17/28

= -17/168

(15/21 : 5/7 ) : (6/5 : 2) 

= 1 : 3/5

= 5/3

a, \(x^2\)  - 19 = 5.9

     \(x^2\) - 19 = 45

     \(x^2\)         = 45 + 19

     \(x^2\)         = 64

      \(x^2\)        = 8²

      \(x\)         = 8 

b, (2\(x\) + 1)³ = -0,001

    (2\(x\) + 1)³ = (-0,1)³

     2\(x\) + 1   = -0,1

     2\(x\)        = -0,1 - 1

     2\(x\)       = - 1,1

       \(x\)      = -1,1: 2

       \(x\)      = -  0,55

\(x^2-19=5\cdot9\\\Rightarrow x^2-19=45\\\Rightarrow x^2=45+19\\\Rightarrow x^2=64\\\Rightarrow x^2=(\pm8)^2\)

\(\Rightarrow\left[{}\begin{matrix}x=8\\x=-8\end{matrix}\right.\)

\(---\)

\((2x+1)^3=-0,001\\\Rightarrow (2x+1)^3=(-0,1)^3\\\Rightarrow2x+1=-0,1\\\Rightarrow2x=-0,1-1\\\Rightarrow2x=-1,1\\\Rightarrow x=-1,1:2\\\Rightarrow x=\dfrac{-11}{20}\\---\)

\(\bigg(\dfrac56\bigg)^{2x-1}=\bigg(\dfrac56\bigg)^5\\\Rightarrow 2x-1=5\\\Rightarrow2x=5+1\\\Rightarrow2x=6\\\Rightarrow x=6:2\\\Rightarrow x=3\\---\)

\(\bigg(\dfrac13x-\dfrac23\bigg)^3=27\\\Rightarrow\bigg(\dfrac13x-\dfrac23\bigg)^3=3^3\\\Rightarrow\dfrac13x-\dfrac23=3\\\Rightarrow\dfrac13x=3+\dfrac23\\\Rightarrow\dfrac13x=\dfrac{11}{3}\\\Rightarrow x=\dfrac{11}{3}:\dfrac13\\\Rightarrow x=11\\---\)

\(\bigg(\dfrac{1}{32}\bigg)^x=\bigg(\dfrac12\bigg)^{15}\\\Rightarrow\bigg(\dfrac{1}{32}\bigg)^x=\bigg[\bigg(\dfrac{1}{2}\bigg)^5\bigg]^3\\\Rightarrow\bigg(\dfrac{1}{32}\bigg)^x=\bigg(\dfrac{1^5}{2^5}\bigg)^3\\\Rightarrow\bigg(\dfrac{1}{32}\bigg)^x=\bigg(\dfrac{1}{32}\bigg)^3\\\Rightarrow x=3\\Toru\)

= 3/4 - 25/6 - 1/8 = -85/24 

= 13/18 - 13/6 + 91/45 = 26/45