(6x-5)/(10x+1) =25/51
306x - 250x = 255+25
x = 5
\(\frac{6x-5}{10x+1}=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{49.51}\)
\(\Rightarrow\frac{6x-5}{10x+1}=\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{49.51}\right)\)
\(\Rightarrow\frac{6x-5}{10x+1}=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{51}\right)\)
\(\Rightarrow\frac{6x-5}{10x+1}=\frac{1}{2}\left(1-\frac{1}{51}\right)\)
\(\Rightarrow\frac{6x-5}{10x+1}=\frac{1}{2}.\frac{50}{51}\)
\(\Rightarrow\frac{6x-5}{10x+1}=\frac{25}{51}\)
\(\Rightarrow\left(6x-5\right).51=\left(10x+1\right).25\)
\(\Rightarrow306x-255=250x+25\)
\(\Rightarrow56x=280\)
\(\Rightarrow x=5\)
Vậy x = 5
