\(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{\left(2x+1\right)\left(2x+3\right)}=\frac{15}{93}\)
\(\frac{1}{2}\left(\frac{1}{3}-\frac{1}{2x+3}\right)=\frac{15}{93}\)
\(\frac{1}{6}-\frac{1}{4x+6}=\frac{15}{93}\)
\(\Rightarrow\frac{4x+6-6}{24x+36}=\frac{15}{93}\)
\(\frac{4x}{4\left(6x+9\right)}=\frac{15}{93}\)
\(\frac{x}{6x+9}=\frac{15}{93}\)
\(\Rightarrow90x+135=93x\)
\(\Rightarrow3x=135\Leftrightarrow x=\frac{135}{3}\)
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