\(\frac{1}{16}=\left(\frac{1}{4}\right)^2=\left(-\frac{1}{4}\right)^2\)

=> \(\left(\frac{1}{3}-2x\right)=\frac{1}{4}\)hoặc \(\left(-\frac{1}{4}\right)\)

*) \(\left(\frac{1}{3}-2x\right)=\frac{1}{4}\)

\(\Rightarrow2x=\frac{1}{3}-\frac{1}{4}=\frac{1}{12}\Rightarrow x=\frac{1}{12}:2=\frac{1}{24}\)

*) \(\left(\frac{1}{3}-2x\right)=\left(-\frac{1}{4}\right)\)

\(\Rightarrow2x=\frac{1}{3}-\left(-\frac{1}{4}\right)=\frac{1}{3}+\frac{1}{4}=\frac{7}{12}\Rightarrow x=\frac{7}{12}:2=\frac{7}{24}\)

Vậy \(x\in\left\{\frac{1}{24};\frac{7}{24}\right\}\)

1/2(2/3.5+2/5.7+2/7.9+...+2/(2x+1)(2x+3))=15/93

1/2(1/3-1/5+1/5-1/7+1/7-1/9+...+1/2x+1-1/2x+3)=15/93

1/2(1/3-1/2x+3)=15/93

=>1/3-1/2x+3=10/31

=>1/2x+3=1/93

=>2x+3=93

2x=93-3=90

=>x=45

Đặt \(A=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{\left(2x+1\right)\left(2x+3\right)}=\frac{15}{93}\)

\(\Rightarrow2A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{\left(2x+1\right)\left(2x+3\right)}=\frac{10}{31}\)

\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2x+1}-\frac{1}{2x+3}=\frac{10}{31}\)

\(\frac{1}{3}-\frac{1}{2x+3}=\frac{10}{31}\)

\(\frac{1}{2x+3}=\frac{1}{3}-\frac{10}{31}\)

\(\frac{1}{2x+3}=\frac{1}{93}\)

\(\Rightarrow2x+3=93\)

\(2x=90\)

\(x=45\)

Vậy \(x=45\).

\(\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{\left(2x+1\right)\left(2x+3\right)}=\frac{15}{93}\)

=> \(\frac{1}{2}\left(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{\left(2x+1\right)\left(2x+3\right)}\right)=\frac{5}{31}\)

=> \(\frac{1}{2}\left(\frac{1}{3}-\frac{1}{2x+3}\right)=\frac{5}{31}\)

=> \(\frac{1}{3}-\frac{1}{2x+3}=\frac{5}{31}:\frac{1}{2}=\frac{5}{31}\cdot2=\frac{10}{31}\)

=> \(\frac{1}{2x+3}=\frac{1}{3}-\frac{10}{31}=\frac{1}{93}\)

=> 2x +3  = 93

=> 2x = 90 => x = 45

\(b)\) \(\left(2x-1\right)^{2012}=\left(2x-1\right)^{2010}\)

\(\Leftrightarrow\)\(\left(2x-1\right)^{2010}.\left(2x-1\right)^2=\left(2x-1\right)^{2010}\)

\(\Leftrightarrow\)\(\left(2x-1\right)^2=1\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}2x-1=1\\2x-1=-1\end{cases}\Leftrightarrow\orbr{\begin{cases}2x=2\\2x=0\end{cases}}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=\frac{2}{2}\\x=\frac{0}{2}\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\\x=0\end{cases}}}\)

Vậy \(x=0\) hoặc \(x=1\)

Chúc bạn học tốt ~ 

\(\left(\frac{1}{x}-\frac{2}{3}\right)^2=\frac{1}{16}\Rightarrow\frac{1}{x}-\frac{2}{3}=\frac{1}{4}\Rightarrow\frac{1}{x}=\frac{11}{12}\Rightarrow x=\frac{12}{11}\)

hoặc \(\frac{1}{x}-\frac{2}{3}=-\frac{1}{4}\Rightarrow\frac{1}{x}=\frac{5}{12}\Rightarrow x=\frac{12}{5}\)

Vậy x = 12/11 , x = 12/5

-5.(x+1/5) -1/2.(x-2/3)=3/2x-5/6

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

-5x-1/2x-3/2x=1+1/3-5/6

x.(-5-1/2-3/2)= 6/6+2/6+(-5/6)

x.(-10/2+(-1/2)+(-3/2))=3/6

x.6/2=1/2

x=1/2:6/2

x=1/6

Vậy x = 1/6

3.(x-1/2) -5(x+3/5)=-x+1/5

3x - 3/2 -5x +3 = -x+1/5 

3x-5x+x= 3/2-3+1/5

x.(3-5+1)=15/10 + (-30/10)+2/10

x.(-1)= -13/10

x = -13/10 : (-1)

x=13/10

vậy x=13/10