A= 6 - 2/3 +1/2 -5 -5/3 + 3/2 - 3 + 7/3 -5/2

A = 6- 5 - 3 - 2/3 -5/3 +7/3 +1/2 + 3/2 -5/2

A= -2 +0 - 1/2

A= -5/2

a: \(=5\cdot5\sqrt{3}-\dfrac{1}{3}\cdot3\sqrt{3}=24\sqrt{3}\)

b: \(=\dfrac{12\left(3+\sqrt{5}\right)}{4}=9+3\sqrt{5}\)

c: \(=3-\sqrt{5}+\sqrt{5}=3\)

Cách 2:

\(A=\left(6-\frac{2}{3}+\frac{1}{2}\right)-\left(5+\frac{5}{3}-\frac{3}{2}\right)-\left(3-\frac{7}{3}+\frac{5}{2}\right)\)

\(=\left(\frac{36}{6}-\frac{4}{6}+\frac{3}{6}\right)-\left(\frac{30}{6}+\frac{10}{6}-\frac{9}{6}\right)-\left(\frac{18}{6}-\frac{14}{6}+\frac{15}{6}\right)\)

\(=\frac{36}{6}-\frac{4}{6}+\frac{3}{6}-\frac{30}{6}-\frac{10}{6}+\frac{9}{6}-\frac{18}{6}+\frac{14}{6}-\frac{15}{6}\)

\(=\frac{36-4+3-30-10+9-18+14-15}{6}\)

\(=-\frac{15}{6}=-\frac{5}{2}\)

a)

\(\begin{array}{l}A = \left( {2 + \frac{1}{3} - \frac{2}{5}} \right) - \left( {7 - \frac{3}{5} - \frac{4}{3}} \right) - \left( {\frac{1}{5} + \frac{5}{3} - 4} \right).\\A = \left( {\frac{{30}}{{15}} + \frac{5}{{15}} - \frac{6}{{15}}} \right) - \left( {\frac{{105}}{{15}} - \frac{9}{{15}} - \frac{{20}}{{15}}} \right) - \left( {\frac{3}{{15}} + \frac{{25}}{{15}} - \frac{{60}}{{15}}} \right)\\A = \frac{{29}}{{15}} - \frac{{76}}{{15}} - \left( {\frac{{ - 32}}{{15}}} \right)\\A = \frac{{29}}{{15}} - \frac{{76}}{{15}} + \frac{{32}}{{15}}\\A = \frac{{ - 15}}{{15}}\\A =  - 1\end{array}\)

b)

\(\begin{array}{l}A = \left( {2 + \frac{1}{3} - \frac{2}{5}} \right) - \left( {7 - \frac{3}{5} - \frac{4}{3}} \right) - \left( {\frac{1}{5} + \frac{5}{3} - 4} \right)\\A = 2 + \frac{1}{3} - \frac{2}{5} - 7 + \frac{3}{5} + \frac{4}{3} - \frac{1}{5} - \frac{5}{3} + 4\\A = \left( {2 - 7 + 4} \right) + \left( {\frac{1}{3} + \frac{4}{3} - \frac{5}{3}} \right) + \left( { - \frac{2}{5} + \frac{3}{5} - \frac{1}{5}} \right)\\A =  - 1 + 0 + 0 =  - 1\end{array}\)

cách 1: A= 35/6 -31/6 -19/6 = -15/6 =-5/2

CÁCH 2: A= 6 -2/3 +1/2 -5 -5/3+ 3/2 -3+7/3 -5/2 

=( 6 - 5 - 3) + (-2/3 - 5/3 +7/3) + (1/2 +3/2 - 5/2)

= - 2 + 0 +  -1/2 = - 5/2

Cách 1: Tính giá trị từng biểu thức trong ngoặc

 A= 

Cách 2: Bỏ dấu ngoặc rồi nhóm các số hạng thích hợp

A =  

   = (6-5-3) -

   = -2 -0 -  = - (2 + ) = -2     

Bài 1: 

a, \(\dfrac{-x-2}{3}\) = - \(\dfrac{6}{7}\)

      - \(x\) - 2 = - \(\dfrac{18}{7}\)

         \(x\)      = - 2 + \(\dfrac{18}{7}\)

         \(x\)      = - \(\dfrac{4}{7}\)

Bài b,  \(\dfrac{4}{7-x}\) = \(\dfrac{1}{3}\)

            12 = 7 - \(x\)

            \(x\)  = 7 - 12 

            \(x\)  = -5 

Bài 2

A = (6 - \(\dfrac{2}{3}\) + \(\dfrac{1}{2}\)) - (5 + \(\dfrac{5}{3}\) - \(\dfrac{3}{2}\)) - (3 - \(\dfrac{7}{3}\) + \(\dfrac{5}{2}\))

A = 6 - \(\dfrac{2}{3}\) + \(\dfrac{1}{2}\) - 5 - \(\dfrac{5}{3}\) + \(\dfrac{3}{2}\) - 3 + \(\dfrac{7}{3}\)  - \(\dfrac{5}{2}\)

A = (6 - 5 - 3) + ( \(\dfrac{1}{2}\) + \(\dfrac{3}{2}\) - \(\dfrac{5}{2}\)) - (\(\dfrac{2}{3}\) + \(\dfrac{5}{3}\) - \(\dfrac{7}{3}\))

A = -2 + (2 - \(\dfrac{5}{2}\)) - 0

A = -2 + 2 - \(\dfrac{5}{2}\)

A = - \(\dfrac{5}{2}\)

Cách 1: = ( 36/6 - 4/6 + 3/6 ) - ( 30/6 + 10/6 - 9/6 ) - ( 18/6 - 14/6 + 15/6 )

            = 35/6 - 31/6 - 19/6

            = -5/2

Cách 2: = 6 - 2/3 + 1/2 - 5 - 5/3 + 3/2 -3 + 7/3 - 5/2

           = ( 6 - 5 - 3 ) + ( -2/3 - 5/3 + 7/3 ) + ( 1/2 + 3/2 - 5/2 )

           = -2 + 0 + -1/2

          = -5/2

Bài 1 :

\(M=\dfrac{30-2^{20}}{2^{18}}=\dfrac{2.15-2^{20}}{2^{18}}=\dfrac{15}{2^{17}}-2^2=\dfrac{15}{2^{17}}-4< 0\left(\dfrac{15}{2^{17}}< 1\right)\)

\(N=\dfrac{3^5}{1^{2021}+2^3}=\dfrac{3^5}{9}=\dfrac{3^5}{3^2}=3^3=27\)

\(\Rightarrow M< N\)

Bài 3 :

a) \(t^2+5t-8\) khi \(t=2\)

\(=5^2+2.5-8\)

\(=25+10-8\)

\(=27\)

b) \(\left(a+b\right)^2-\left(b-a\right)^3+2021\left(1\right)\)

\(\left\{{}\begin{matrix}a=5\\b=a+1=6\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a+b=11\\b-a=1\end{matrix}\right.\)

\(\left(1\right)=11^2-1^3+2021=121-1+2021=2141\)

c) \(x^3-3x^2y+3xy^2-y^3=\left(x-y\right)^3\left(1\right)\)

\(\left\{{}\begin{matrix}x=3\\y=2\end{matrix}\right.\) \(\Rightarrow x-y=1\)

\(\left(1\right)=1^3=1\)

Bài 2 :

a) \(...=2^3\left(19-14\right)+1=8.5+1=41\)

b) \(...=100-\left[60:\left(5^2-15\right)\right]=100-\left[60:10\right]=100-6=94\)

c) \(...=160:\left[17+\left(9.5-\left(14+2^3\right)\right)\right]=160:\left[17+\left(45-22\right)\right]=160:\left[17+23\right]=160:40=4\)

d) \(...=798+100\left[16-2\left(25-22\right)\right]=798+100\left[16-2.3\right]=798+100.10=798+1000=1798\)