\(\frac{x+12}{7}+\frac{x+4}{15}+\frac{x+6}{13}=\frac{x+8}{11}+\frac{x+10}{9}+\frac{x+12}{7}\)
=>\(\left(\frac{x+12}{7}+1\right)+\left(\frac{x+4}{15}+1\right)+\left(\frac{x+6}{13}+1\right)=\left(\frac{x+8}{11}+1\right)+\left(\frac{x+10}{9}+1\right)+\left(\frac{x+12}{7}+1\right)\)
=> \(\frac{x+19}{7}+\frac{x+19}{15}+\frac{x+19}{13}=\frac{x+19}{11}+\frac{x+19}{9}+\frac{x+19}{7}\)
=> \(\frac{x+19}{7}+\frac{x+19}{15}+\frac{x+19}{13}-\frac{x+19}{11}-\frac{x+19}{9}-\frac{x+19}{7}=0\)
\(\Rightarrow\left(x+19\right)\left(\frac{1}{7}+\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}-\frac{1}{7}\right)=0\)
=> x + 19 = 0 Vì \(\frac{1}{7}+\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}-\frac{1}{7}\ne0\)
=> x = - 19
Bài làm:
Ta có: \(\frac{x+12}{7}+\frac{x+4}{15}+\frac{x+6}{13}=\frac{x+8}{11}+\frac{x+10}{9}+\frac{x+12}{7}\)
\(\Leftrightarrow\left(\frac{x+12}{7}+1\right)+\left(\frac{x+4}{15}+1\right)+\left(\frac{x+6}{13}+1\right)-\left(\frac{x+8}{11}+1\right)-\left(\frac{x+10}{9}+1\right)-\left(\frac{x+12}{7}+1\right)=0\)
\(\Leftrightarrow\frac{x+19}{7}+\frac{x+19}{15}+\frac{x+19}{13}-\frac{x+19}{11}-\frac{x+19}{9}-\frac{x+19}{7}=0\)
\(\Leftrightarrow\left(x+19\right)\left(\frac{1}{7}+\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}-\frac{1}{7}\right)=0\)
\(\Leftrightarrow\left(x+19\right)\left(\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}\right)=0\)
Mà \(\hept{\begin{cases}\frac{1}{15}< \frac{1}{11}\\\frac{1}{13}< \frac{1}{9}\end{cases}\Rightarrow}\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}< 0\)
\(\Rightarrow x+19=0\)
\(\Rightarrow x=-19\)
\(\frac{x+12}{7}+\frac{x+4}{15}+\frac{x+6}{13}=\frac{x+8}{11}+\frac{x+10}{9}+\frac{x+12}{7}\)
\(\Leftrightarrow\left(\frac{x+12}{7}+1\right)+\left(\frac{x+4}{15}+1\right)+\left(\frac{x+6}{13}+1\right)=\left(\frac{x+8}{11}+1\right)+\left(\frac{x+10}{9}+1\right)+\left(\frac{x+12}{7}+1\right)\)
\(\Leftrightarrow\frac{x+12+7}{7}+\frac{x+4+15}{15}+\frac{x+6+13}{13}=\frac{x+8+11}{11}+\frac{x+10+9}{9}+\frac{x+12+7}{7}\)
\(\Leftrightarrow\frac{x+19}{7}+\frac{x+19}{15}+\frac{x+19}{13}=\frac{x+19}{11}+\frac{x+19}{9}+\frac{x+19}{7}\)
\(\Leftrightarrow\frac{x+19}{7}+\frac{x+19}{15}+\frac{x+19}{13}-\frac{x+19}{11}-\frac{x+19}{9}-\frac{x+19}{7}=0\)
\(\Leftrightarrow\left(x+19\right)\left(\frac{1}{7}+\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}-\frac{1}{7}\right)=0\)
Vì \(\frac{1}{7}+\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}-\frac{1}{7}\ne0\)
\(\Rightarrow x+19=0\Leftrightarrow x=-19\)
\(\frac{x+12}{7}+\frac{x+4}{15}+\frac{x+6}{13}=\frac{x+8}{11}+\frac{x+10}{9}+\frac{x+12}{7}\)
<=> \(\left(\frac{x+12}{7}+1\right)+\left(\frac{x+4}{15}+1\right)+\left(\frac{x+6}{13}+1\right)=\left(\frac{x+8}{11}+1\right)+\left(\frac{x+10}{9}+1\right)+\left(\frac{x+12}{7}+1\right)\)
<=> \(\frac{x+19}{7}+\frac{x+19}{15}+\frac{x+19}{13}=\frac{x+19}{11}+\frac{x+19}{9}+\frac{x+19}{7}\)
<=> \(\frac{x+19}{7}+\frac{x+19}{15}+\frac{x+19}{13}-\frac{x+19}{11}-\frac{x+19}{9}-\frac{x+19}{7}=0\)
<=> \(\left(x+19\right)\left(\frac{1}{7}+\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}-\frac{1}{7}\ne0\right)=0\)
<=> \(x+19=0\)<=> \(x=-19\)
