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\(\frac{25^3.4^6.3^{12}}{75^5.8^4}\)

\(\text{Hok nhìu wa máu dồn đến não~~`~ quên hết}\)

Ta có:\(\frac{25^3.4^6.3^{12}}{75^5.8^4}=\frac{25^3.4^6.3^{12}}{25^5.3^5.2^4.4^4}\)\(=\frac{4^2.3^7}{25^2.2^4}\)\(=\frac{2^2.2^2.3^7}{25^2.2^4}\)\(=\frac{3^7}{25^2}\)\(=\frac{2187}{625}\)

\(\frac{x+4}{2014}+\frac{x+3}{2015}=\frac{x+2}{2016}+\frac{x+1}{2017}\) 

\(\Leftrightarrow\frac{x+4}{2014}+1+\frac{x+3}{2015}+1=\frac{x+2}{2016}+1+\frac{x+1}{2017}+1\)

\(\Leftrightarrow\frac{x+2018}{2014}+\frac{x+2018}{2015}=\frac{x+2018}{2016}+\frac{x+2018}{2017}\) 

\(\Leftrightarrow\frac{x+2018}{2014}+\frac{x+2018}{2015}-\frac{x+2018}{2016}-\frac{x+2018}{2017}=0\) 

\(\Leftrightarrow\left(x+2018\right)\left(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2016}-\frac{1}{2017}\right)=0\)  

Vì: \(\frac{1}{2014}+\frac{1}{2015}-\frac{1}{2016}-\frac{1}{2017}\ne0\) 

\(\Rightarrow x+2018=0\Rightarrow x=-2018\)

\(\frac{6x-5}{-7}=\frac{5x-3}{-5}\)

=> (6x - 5).(-5) = (5x - 3).(-7)

=> -30x + 25 = -35x + 21

=> -30x + 35x = 21 - 25

=> 5x = -4

=> \(x=-\frac{4}{5}\)

|2x - 1| = |2x + 3|

=> \(\orbr{\begin{cases}2x-1=2x+3\\2x-1=-\left(2x+3\right)\end{cases}}\)=> \(\orbr{\begin{cases}2x-2x=3+1\\2x-1=-2x-3\end{cases}}\)=> \(\orbr{\begin{cases}0=4\\2x+2x=-3+1\end{cases}}\)

Mà \(0\ne4\Rightarrow4x=-2\)

=> \(x=-\frac{2}{4}=-\frac{1}{2}\)