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\(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{x\left(x+2\right)}=\frac{11}{75}\)
\(\Leftrightarrow\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{11}{75}\)
\(\Leftrightarrow\frac{1}{3}-\frac{1}{x+2}=\frac{11}{75}:\frac{1}{2}=\frac{22}{75}\Leftrightarrow\frac{1}{x+2}=\frac{1}{25}\Leftrightarrow x=23\)
Bài làm
\(\frac{1}{2}.\frac{x+3}{5}.\left(x-2\right)=3\)
Bài làm
xl, vừa r bấm nhầm.
\(\frac{1}{2}.\frac{x+3}{5}.\left(x-2\right)=3\)
\(\frac{x+3}{10}.\left(x-2\right)=3\)
\(\frac{x^2-2x+3x-6}{10}=3\)
\(x^2-2x+3x-6=3.10\)
\(x^2+x-6=30\)
\(x^2+x-36=0\)
\(\frac{1}{3}+\frac{2}{5}\left(x+1\right)=1\)
\(\Leftrightarrow\frac{2}{5}\left(x+1\right)=\frac{2}{3}\)
\(\Leftrightarrow x+1=\frac{5}{3}\)
\(\Leftrightarrow x=\frac{2}{3}\)
\(\frac{1}{3}+\frac{2}{5}.\left(x+1\right)=1\)
\(\frac{2}{5}.\left(x+1\right)=1-\frac{1}{3}\)
\(\frac{2}{5}.\left(x+1\right)=\frac{2}{3}\)
\(x+1=\frac{2}{3}:\frac{2}{5}\)
\(x+1=\frac{5}{3}\)
\(x=\frac{5}{3}-1\)
\(x=\frac{2}{3}\)