\(\frac{3}{5.7}+\frac{3}{7.9}+...+\frac{3}{x.\left(x+2\right)}=\frac{24}{35}\)
\(\frac{3}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{x.\left(x+2\right)}\right)=\frac{24}{35}\)
\(\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{x+2}\right)=\frac{24}{35}\)
\(\frac{3}{10}-\frac{3}{2x+4}=\frac{24}{35}\)
\(\frac{3}{2x+4}=\frac{-27}{70}\)
tự làm nốt
\(\frac{3}{35}+\frac{3}{63}+\frac{3}{99}+....+\frac{3}{x\left(x+2\right)}=\frac{24}{35}\)
\(\Leftrightarrow3\left(\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+....+\frac{1}{x\left(x+2\right)}\right)=\frac{24}{25}\)
\(\Leftrightarrow3\left(\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+...+\frac{1}{x\left(x+2\right)}\right)=\frac{24}{35}\)
\(\Leftrightarrow3\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+....+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{24}{35}\)
\(\Leftrightarrow3\left(\frac{1}{5}-\frac{1}{x+2}\right)=\frac{24}{35}\)
\(\Leftrightarrow\frac{3}{5}-\frac{3}{x+2}=\frac{24}{35}\)
\(\Leftrightarrow\frac{3}{x+2}=\frac{3}{5}-\frac{24}{35}\)
\(\Leftrightarrow\frac{3}{x+2}=\frac{21-24}{35}\)
\(\Leftrightarrow\frac{3}{x+2}=\frac{3}{-35}\)
\(\Rightarrow x+2=-35\Leftrightarrow x=-35-2\Leftrightarrow x=-37\)
Vậy \(x=-37\)
