\(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+...+\frac{1}{\left(2x+1\right)\left(2x+3\right)}=\frac{15}{93}\)
\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{\left(2x+1\right)\left(2x+3\right)}=\frac{15}{93}\)
\(\frac{1}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{\left(2x+1\right)\left(2x+3\right)}\right)=\frac{15}{93}\)
\(\frac{1}{2}\)\(\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2x+1}-\frac{1}{2x+3}\right)\)\(=\frac{15}{93}\)
\(\frac{1}{2}\left(\frac{1}{3}-\frac{1}{2x+3}\right)=\frac{15}{93}\)
\(\frac{1}{3}-\frac{1}{2x+3}=\frac{15}{93}:\frac{1}{2}=\frac{10}{31}\)
\(\frac{1}{2x+3}=\frac{1}{3}-\frac{10}{31}=\frac{1}{93}\)
\(\Rightarrow2x+3=93\rightarrow2x=90\rightarrow x=45\)
