\(\frac{x}{2}-\left(\frac{3}{5}x-\frac{13}{5}\right)=-\left(\frac{7}{5}+\frac{7}{10}x\right)\)

\(\Rightarrow\frac{5x-6x+26+14+7x}{10}=0\Rightarrow6x+40=0\Rightarrow x=-\frac{20}{3}\)

A) \(\frac{7}{\left(x+3\right)\left(x+10\right)}+\frac{11}{\left(x+10\right)\left(x+21\right)}+\frac{13}{\left(x+21\right)\left(x+34\right)}\)

\(=\frac{\left(x+10\right)-\left(x+3\right)}{\left(x+3\right)\left(x+10\right)}+\frac{\left(x+21\right)-\left(x+10\right)}{\left(x+10\right)\left(x+21\right)}+\frac{\left(x+34\right)-\left(x+21\right)}{\left(x+21\right)\left(x+34\right)}\)

\(=\frac{1}{x+3}-\frac{1}{x+10}+\frac{1}{x+10}-\frac{1}{x+21}+\frac{1}{x+21}-\frac{1}{x+34}\)

\(=\frac{1}{x+3}-\frac{1}{x+34}\)

\(=\frac{\left(x+34\right)-\left(x+3\right)}{\left(x+3\right)\left(x+34\right)}\)\(=\frac{x}{\left(x+3\right)\left(x+34\right)}\)

\(\Rightarrow\left(x+34\right)-\left(x+3\right)=x\)

\(\Rightarrow x=31\)

Vậy, x = 31 

Bạn áp dụng: \(\frac{k}{x\cdot\left(x+k\right)}=\frac{1}{x}-\frac{1}{x+k}\) với    \(x,k\inℝ;x\ne0;x\ne-k\)

Chứng minh: \(\frac{1}{x}-\frac{1}{x+k}=\frac{x+k}{x\left(x+k\right)}-\frac{x}{x\left(x+k\right)}=\frac{x+k-x}{x\left(x+k\right)}=\frac{k}{x\left(x+k\right)}\)

B) \(\frac{\left(x-4\right)-\left(x-7\right)}{\left(x-7\right)\left(x-4\right)}+\frac{\left(x-7\right)-\left(x-13\right)}{\left(x-13\right)\left(x-7\right)}+\frac{\left(x-13\right)-\left(x-28\right)}{\left(x-28\right)\left(x-13\right)}\)

\(=\frac{1}{x-7}-\frac{1}{x-4}+\frac{1}{x-13}-\frac{1}{x-7}+\frac{1}{x-28}-\frac{1}{x-13}\)

\(=\frac{1}{x-28}-\frac{1}{x-4}=-\frac{5}{2}+\frac{1}{x-28}\)

\(\Leftrightarrow\frac{1}{x-28}-\frac{1}{x-4}-\frac{1}{x-28}=-\frac{5}{2}\)

\(\Leftrightarrow\frac{1}{x-4}=\frac{5}{2}\)

=> 5x - 20 = 2

=> 5x = 22 

\(\Rightarrow x=\frac{22}{5}=4,4\)

Vậy, x = 4,4

\(\left(\frac{13}{21}+x\right).\frac{7}{12}=\frac{13}{15}-\frac{7}{10}\)
\(\left(\frac{13}{21}+x\right).\frac{7}{12}=\frac{26}{30}-\frac{21}{30}\)
\(\left(\frac{13}{21}+x\right).\frac{7}{12}=\frac{1}{6}\)

​\(\frac{13}{21}+x=\frac{1}{6}:\frac{7}{12}\)​​​​

\(\frac{13}{21}+x=\frac{1.12}{6.7}\)
\(\frac{13}{21}+x=\frac{2}{7}\)
\(x=\frac{2}{7}-\frac{13}{21}\)
\(x=\frac{6}{21}-\frac{13}{21}\)
\(x=\frac{-1}{3}\)

\(\frac{13}{15}-\left(\frac{13}{21}+x\right).\frac{7}{12}=\frac{7}{10}\)

\(\left(\frac{13}{21}+x\right).\frac{7}{12}=\frac{13}{15}-\frac{7}{10}\)

\(\left(\frac{13}{21}+x\right).\frac{7}{12}=\frac{1}{6}\)

\(\frac{13}{21}+x=\frac{1}{6}:\frac{7}{12}\)

\(\frac{13}{21}+x=\frac{2}{7}\)

\(x=\frac{2}{7}-\frac{13}{21}\)

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

\(\frac{1}{2}+\frac{5}{6}-\frac{3}{8}\)

\(=\frac{12}{24}+\frac{20}{24}-\frac{9}{24}\)

\(=\frac{23}{24}\)

\(\frac{10}{15}\cdot\frac{7}{4}+\frac{7}{4}\cdot\frac{9}{15}-\frac{4}{15}\cdot\frac{7}{4}\)

\(=\frac{7}{4}\cdot\left(\frac{10}{15}+\frac{9}{15}-\frac{4}{15}\right)\)

\(=\frac{7}{4}\cdot1=\frac{7}{4}\)

\(\left(\frac{4}{5}+\frac{1}{2}\right)\left(\frac{3}{13}-\frac{8}{13}\right)\)

\(=\left(\frac{8}{10}+\frac{5}{10}\right)\cdot\left(-\frac{5}{13}\right)\)

\(=\frac{13}{10}\cdot\left(-\frac{5}{13}\right)=-\frac{1}{2}\)

a,  3x-12 = 30 

=> 3x = 30 + 12

=> 3x = 42 

=> x = 42 : 3  = 14 

Vậy x = 14 

b, \(\frac{2}{3}x+\frac{1}{4}=\frac{7}{12}\)

\(\Rightarrow\frac{2}{3}x=\frac{7}{12}-\frac{1}{4}\)

\(\Rightarrow\frac{2}{3}x=\frac{7}{12}-\frac{3}{12}\)

\(\Rightarrow\frac{2}{3}x=\frac{1}{3}\)

\(\Rightarrow x=\frac{1}{3}\div\frac{2}{3}\Rightarrow\frac{1}{3}\cdot\frac{3}{2}=\frac{1}{2}\)

Vậy x = \(\frac{1}{2}\)

c, 2x² = 32 

=> x² = 32 : 2 

=> x² = 16

=> x² = 4² 

=> x = 4 

Vậy x = 4 

thanhks anh nhé!