\(\frac{x+1}{96}+\frac{x+2}{95}=\frac{x+3}{94}+\frac{x+4}{93}\)
\(\Rightarrow\left(\frac{x+1}{96}+1\right)+\left(\frac{x+2}{95}+1\right)=\left(\frac{x+3}{94}+1\right)+\left(\frac{x+4}{93}+1\right)\)
\(\Rightarrow\frac{x+97}{96}+\frac{x+97}{95}=\frac{x+97}{94}+\frac{x+97}{93}\)
\(\Rightarrow\frac{x+97}{96}+\frac{x+97}{95}-\frac{x+97}{94}-\frac{x+97}{93}=0\)
\(\Rightarrow\left(x+97\right)\left(\frac{1}{96}+\frac{1}{95}-\frac{1}{94}-\frac{1}{93}\right)=0\)
Mà \(\frac{1}{96}+\frac{1}{95}-\frac{1}{94}-\frac{1}{93}\ne0\)
\(\Rightarrow x+97=0\)
\(\Rightarrow x=-97\)
Vậy x = -97
Có : \(\frac{x+1}{96}+\frac{x+2}{95}=\frac{x+3}{94}+\frac{x+4}{93}\)
\(\Leftrightarrow\)\(\left(\frac{x+1}{96}+1\right)+\left(\frac{x+2}{95}+1\right)\)= \(\left(\frac{x+3}{94}+1\right)+\left(\frac{x+4}{93}+1\right)\)
\(\Leftrightarrow\) \(\frac{x+97}{96}+\frac{x+97}{95}=\frac{x+97}{94}+\frac{x+97}{93}\)
\(\Leftrightarrow\) \(\frac{x+97}{96}+\frac{x+97}{95}-\frac{x+97}{94}-\frac{x+97}{93}=0\)
\(\Leftrightarrow\) \(\left(x+97\right)\left(\frac{1}{96}+\frac{1}{95}-\frac{1}{94}-\frac{1}{93}\right)=0\)
\(\Leftrightarrow\) \(\left(x+97\right)=0\) ( \(\frac{1}{96}+\frac{1}{95}-\frac{1}{94}-\frac{1}{93}\)) \(\ne0\)
\(\Leftrightarrow\)\(x=-97\)
Vậy \(x=-97\)
