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)

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

đầy đủ phần ngoặc hay gì đó

\(\dfrac{11}{2}\): \(\dfrac{1}{4}\) \(\times\) \(\dfrac{5}{3}\)

= \(\dfrac{11}{2}\) \(\times\) \(\dfrac{4}{1}\) \(\times\) \(\dfrac{5}{3}\)

= 22 \(\times\) \(\dfrac{5}{3}\)

= \(\dfrac{110}{3}\)

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

= \(\dfrac{30}{12}-\dfrac{3}{12}+\dfrac{20}{12}\)

= \(\dfrac{7}{12}\) 

\(\dfrac{14}{5}\times\dfrac{2}{3}\)+ 5

= \(\dfrac{28}{15}\) + 5

= \(\dfrac{28}{15}\) + \(\dfrac{75}{15}\)

= \(\dfrac{103}{15}\)

1. ĐKXĐ: \(x\ne\pm1\)

2. \(A=\left(\dfrac{x+1}{x-1}-\dfrac{x+3}{x+1}\right)\cdot\dfrac{x+1}{2}\)

\(=\dfrac{\left(x+1\right)^2-\left(x-3\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{x+1}{2}\)

\(=\dfrac{x^2+2x+1-x^2+4x-3}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{x+1}{2}\)

\(=\dfrac{6x-2}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{x+1}{2}\)

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

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

3. Tại x = 5, A có giá trị là:

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

4. \(A=\dfrac{x-3}{x-1}\) \(=\dfrac{x-1-3}{x-1}=1-\dfrac{3}{x-1}\)

Để A nguyên => \(3⋮\left(x-1\right)\) hay \(\left(x-1\right)\inƯ\left(3\right)=\left\{1;-1;3;-3\right\}\)

\(\Rightarrow\left\{{}\begin{matrix}x-1=1\\x-1=-1\\x-1=3\\x-1=-3\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=2\left(tmđk\right)\\x=0\left(tmđk\right)\\x=4\left(tmđk\right)\\x=-2\left(tmđk\right)\end{matrix}\right.\)

Vậy: A nguyên khi \(x=\left\{2;0;4;-2\right\}\)

Bài 3 : 

Vì \(\left(x-2\right)^2\ge0\forall x\)

Nên :  \(A=\left(x-2\right)^2-4\ge-4\forall x\)

Vậy \(A_{min}=-4\) khi x = 2

B1: lấy máy tính mà tính thôi bạn (nhớ lm theo từng bước)

B2: 

a, \(\left|x-\frac{2}{3}\right|-\frac{1}{2}=\frac{5}{6}\)

\(\left|x-\frac{2}{3}\right|=\frac{4}{3}\)

\(\Rightarrow\orbr{\begin{cases}x-\frac{2}{3}=\frac{4}{3}\\x-\frac{2}{3}=\frac{-4}{3}\end{cases}\Rightarrow\orbr{\begin{cases}x=2\\x=\frac{-2}{3}\end{cases}}}\)

b, \(\frac{\left(-2\right)^x}{512}=-32\Rightarrow\left(-2\right)^x=-16384\Rightarrow x\in\varnothing\)

B3:

Vì \(\left(x-2\right)^2\ge0\Rightarrow A=\left(x-2\right)^2-4\ge-4\)

Dấu "=" xảy ra khi x = 2

Vậy GTNN của A = -4 khi x = 2

a: \(=\dfrac{3}{5}\cdot\dfrac{5}{4}+\dfrac{1}{2}\cdot\dfrac{2}{3}=\dfrac{3}{4}+\dfrac{1}{3}=\dfrac{9+4}{12}=\dfrac{13}{12}\)

b: \(\Leftrightarrow x\cdot\dfrac{5}{4}=\dfrac{5}{8}\)

hay x=1/2

lần này mới được à

? Lần này mới được

a: =6x2/5-3/10

=12/5-3/10

=24/10-3/10=21/10

b: =1/2+4/3=3/6+8/6=11/6

c: =5/6+1/4=10/12+3/12=13/12

a: \(x:5=\dfrac{15}{14}\\ \Rightarrow x=\dfrac{15}{70}=\dfrac{3}{14}\)

a) \(x:5=\dfrac{4}{7}+\dfrac{1}{2}\)

\(\dfrac{x}{5}=\dfrac{15}{14}\)

\(\Rightarrow x=\dfrac{5.15}{14}=\dfrac{75}{14}\)

b) \(\dfrac{1}{3}+\dfrac{2}{9}\times\dfrac{3}{4}=\dfrac{1}{3}+\dfrac{1}{6}=\dfrac{2}{6}+\dfrac{1}{6}=\dfrac{3}{6}=\dfrac{1}{2}\)

\(x\div5=\dfrac{4}{7}+\dfrac{1}{2}\)

\(x\div5=\dfrac{15}{14}\)

\(x=\dfrac{15}{14}\times5\)

\(x=\dfrac{75}{14}\)

b)

\(\dfrac{1}{3}+\dfrac{2}{9}\times\dfrac{3}{4}\)

\(=\dfrac{1}{3}+\dfrac{1}{6}\)

\(=\dfrac{1}{2}\)

\(2\dfrac{1}{20}\)

\(\dfrac{13}{18}\)

4/5 + 5/4 = 16/20 + 25/20 = 41/20

1/2 + 2/9 = 9/18 + 4/18 = 13/18

Thanks kiuuuu

\(A=1.3+2.4+3.5+....+48.50\)

\(A=1.\left(1+2\right)+2.\left(3+1\right)+3.\left(4+1\right)+....+48.\left(49+1\right)\)

\(A=1.2+1+2.3+2+3.4+3+....+48.49+48\)

\(A\left(=1.2+2.3+...+48.49\right)+\left(1+2+...+48\right)\)

tự làm tiếp :))

p/s: ck iu :3 

A=(48.50.51-1.3.0):3=.....