\(\frac{x-971}{972}+\frac{x-973}{970}+\frac{x-975}{968}+\frac{x-977}{966}=\frac{x-972}{971}+\frac{x-970}{973}+\frac{x-968}{975}+\frac{x-966}{977}\)
\(\Rightarrow\frac{x-971}{972}-1+\frac{x-973}{970}-1+\frac{x-975}{968}-1+\frac{x-977}{966}-1=\frac{x-972}{971}-1+\frac{x-970}{973}-1+\frac{x-968}{975}-1+\frac{x-966}{977}-1\)\(\Rightarrow\frac{x-1943}{972}+\frac{x-1943}{970}+\frac{x-1943}{968}+\frac{x-1943}{966}=\frac{x-1943}{971}+\frac{x-1943}{973}+\frac{x-1943}{975}+\frac{x-966}{977}\)
\(\Leftrightarrow\frac{x-1943}{972}+\frac{x-1943}{970}+\frac{x-1943}{968}+\frac{x-1943}{966}-\frac{x-1943}{971}-\frac{x-1943}{973}-\frac{x-1943}{975}-\frac{x-966}{977}=0\)
\(\Leftrightarrow\left(x-1943\right).\left(\frac{1}{972}+\frac{1}{970}+\frac{1}{968}+\frac{1}{966}-\frac{1}{971}-\frac{1}{973}+\frac{1}{975}+\frac{1}{977}\right)=0\)
\(\Leftrightarrow\left(x-1943\right)=0\Leftrightarrow x=1943\)
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