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1. \(x=\frac{61}{42}\)
2. \(x=\frac{-36}{5}\)
3. \(x=\frac{13}{11}\)
4. \(x=\frac{1}{12}\)
5.\(x=\frac{-5}{2}\)

\(x\times\frac{6}{25}=\frac{15}{-13}\)
x=\(\frac{15}{-13}\div\frac{6}{25}\)
x=\(-\frac{125}{26}\)
các câu còn lại làm tương tự nha!!!
\(1.x.\frac{6}{25}=\frac{15}{-13}\\ x=\frac{15}{-13}:\frac{6}{25}\\ x=-\frac{125}{26}\)
\(2.x:\frac{4}{10}=\frac{13}{-45}+\frac{8}{15}\\ x:\frac{4}{10}=\frac{11}{45}\\ x=\frac{11}{45}.\frac{4}{10}\\ x=\frac{22}{225}\)
\(3.\frac{3}{8}-\frac{1}{6}.x=\frac{1}{4}\\ \frac{1}{6}.x=\frac{3}{8}-\frac{1}{4}\\ \frac{1}{6}.x=\frac{1}{8}\\ x=\frac{1}{8}:\frac{1}{6}\\ x=\frac{3}{4}\)
\(4.\frac{1}{3}+\frac{1}{2}:x=-4\\ \frac{1}{2}:x=-4-\frac{1}{3}=-\frac{13}{3}\\ x=\frac{1}{2}:\left(-\frac{13}{3}\right)=-\frac{3}{26}\)
\(5.x+\frac{7}{12}=\frac{17}{18}-\frac{1}{9}=\frac{5}{6}\\ x=\frac{5}{6}-\frac{7}{12}\\ x=\frac{1}{4}\)

a)\(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\Leftrightarrow\left(x-1\right)^{x+2}\left[\left(x-1\right)^2-1\right]=0\Leftrightarrow x\left(x-1\right)^{x+2}\left(x-2\right)=0\)
Do đó \(x\in\left\{0;1;2\right\}\)
b)
\(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot...\cdot\frac{31}{64}=2^x\Leftrightarrow\frac{1\cdot2\cdot3\cdot...\cdot31}{4\cdot6\cdot8\cdot...\cdot64}=2^x\Leftrightarrow\frac{31!}{\left(2\cdot2\right)\cdot\left(2\cdot3\right)\cdot\left(2\cdot4\right)\cdot...\cdot\left(2\cdot31\right)\cdot64}=2^x\)
\(\frac{31!}{2^{30}\cdot31!\cdot2^6}=2^x\Leftrightarrow\frac{1}{2^{36}}=2^x\Leftrightarrow2^{-36}=2^x\Rightarrow x=-36\)

Bài 1:
a) Ta có: \(\frac{5}{6}-\frac{2}{3}+\frac{1}{4}\)
\(=\frac{10}{12}-\frac{8}{12}+\frac{3}{12}\)
\(=\frac{2+3}{12}=\frac{5}{12}\)
b) Ta có: \(1\frac{11}{12}-\frac{5}{12}\cdot\left(\frac{4}{5}-\frac{1}{10}\right):\frac{-5}{12}\)
\(=\frac{23}{12}-\frac{5}{12}\cdot\left(\frac{8}{10}-\frac{1}{10}\right)\cdot\frac{-12}{5}\)
\(=\frac{23}{12}-\frac{5}{12}\cdot\frac{7}{10}\cdot\frac{-12}{5}\)
\(=\frac{23}{12}-\frac{-7}{10}\)
\(=\frac{115}{60}+\frac{42}{60}=\frac{157}{60}\)
Bài 2:
a) Ta có: \(\frac{1}{2}\cdot x-\frac{2}{5}=\frac{1}{5}\)
\(\Leftrightarrow\frac{1}{2}\cdot x=\frac{1}{5}+\frac{2}{5}=\frac{3}{5}\)
\(\Leftrightarrow x=\frac{3}{5}:\frac{1}{2}=\frac{3}{5}\cdot2=\frac{6}{5}\)
Vậy: \(x=\frac{6}{5}\)
b) Ta có: \(\left(1-2x\right)\cdot\frac{4}{3}=\left(-2\right)^3\)
\(\Leftrightarrow\left(1-2x\right)\cdot\frac{4}{3}=-8\)
\(\Leftrightarrow1-2x=-8:\frac{4}{3}=-8\cdot\frac{3}{4}=-6\)
\(\Leftrightarrow-2x=-6-1=-7\)
hay \(x=\frac{7}{2}\)
Vậy: \(x=\frac{7}{2}\)

\(a,\frac{2}{3}.\left(3-x\right)+\frac{1}{2}=\frac{3}{4}.\left(2.x+1\right)
\)
\(2-\frac{2}{3}x+\frac{1}{2}=\frac{3}{2}.\frac{3}{4}x+\frac{3}{4}
\)
\(\frac{2}{3}x+2-\frac{1}{2}=\frac{9}{8}x+\frac{3}{4}\)
\(\frac{2}{3}x+\frac{3}{2}=\frac{9}{8}x+\frac{3}{4}\)
\(\frac{3}{2}-\frac{3}{4}=\frac{9}{8}x-\frac{2}{3}x\)
\(\frac{6}{4}-\frac{3}{4}=\frac{27}{24}x-\frac{16}{24}x\)
\(\frac{11}{24}x=\frac{3}{4}\)
\(x=\frac{3}{4}:\frac{11}{24}\)
\(x=\frac{3}{4}.\frac{24}{11}\)
\(x=\frac{18}{11}\)
\(Vậy
x=\frac{18}{11}\)
\(b,\frac{5-x}{3}=\frac{2x+1}{5}\)
\(\frac{\left(5-x\right).5}{15}=\frac{\left(2x+1\right).3}{15}\)
\(\Rightarrow\left(5-x\right).5=\left(2x+1\right).3\)
\(25-5x=6x+3\)
\(25-3=6x+5x\)
\(\Rightarrow11x=22\)
\(\Rightarrow x=22:11\)
\(\Rightarrow x=2\)
\(Vậy
x=2\)
Bạn chỉ mình cách viết hỗn số đi rồi mình sẽ chỉ bài cho
\(2\frac{5}{6}.x-\frac{3}{2}=3\frac{5}{6}\)
\(\Rightarrow\)\(2\frac{5}{6}.x=3\frac{5}{6}+\frac{3}{2}\)
\(\Rightarrow\)\(2\frac{5}{6}.x=\frac{16}{3}\)
\(\Rightarrow\)\(x=\frac{16}{3}:2\frac{5}{6}\)
\(\Rightarrow\)\(x=\frac{32}{17}\)