Ta có : \(\frac{x-1}{99}+\frac{x-3}{97}=\frac{x-4}{96}+\frac{x-6}{94}\)
\(\Leftrightarrow\left(\frac{x-1}{99}-1\right)+\left(\frac{x-3}{97}-1\right)=\left(\frac{x-4}{96}-1\right)+\left(\frac{x-6}{94}-1\right)\)
\(\Leftrightarrow\frac{x-100}{99}+\frac{x-100}{97}=\frac{x-100}{96}+\frac{x-100}{94}\)
\(\Leftrightarrow\frac{x-100}{99}+\frac{x-100}{97}-\frac{x-100}{96}-\frac{x-100}{94}=0\)
\(\Leftrightarrow\left(x-100\right)\left(\frac{1}{99}+\frac{1}{97}-\frac{1}{96}-\frac{1}{94}\right)=0\)
Mà \(\left(\frac{1}{99}+\frac{1}{97}-\frac{1}{96}-\frac{1}{94}\right)\ne0\)
Nên : \(x-100=0\)
Suy ra : \(x=100\)
\(\frac{x-1}{99}+\frac{x-3}{97}=\frac{x-4}{96}+\frac{x-6}{94}\)
\(\Leftrightarrow\frac{x-1}{99}-1+\frac{x-3}{97}-1=\frac{x-4}{96}-1+\frac{x-6}{94}-1\)
\(\Leftrightarrow\frac{x-100}{99}+\frac{x-100}{97}-\frac{x-100}{94}-\frac{x-100}{96}=0\)
\(\Leftrightarrow\left(x-100\right)\left(\frac{1}{99}+\frac{1}{97}-\frac{1}{94}-\frac{1}{96}\right)=0\)
<=>x-100=0
<=>x=100
\(\frac{x-1}{99}+\frac{x-3}{97}=\frac{x-4}{96}+\frac{x-6}{94}\)
\(\Leftrightarrow\frac{x-1}{99}-1+\frac{x-3}{97}-1=\frac{x-4}{96}-1+\frac{x-6}{94}-1\)
\(\Leftrightarrow\frac{x-100}{99}+\frac{x-100}{97}=\frac{x-100}{96}+\frac{x-100}{94}\)
\(\Rightarrow\frac{x-100}{99}+\frac{x-100}{97}-\frac{x-100}{96}-\frac{x-100}{94}=0\)
\(\Rightarrow\left(x-100\right)\left(\frac{1}{99}+\frac{1}{97}-\frac{1}{96}-\frac{1}{94}\right)=0\)
<=> x - 100 = 0
<=> x = 100
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