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\frac{1}{0.2+100+0.2}
Subtract 0.8 from 1 to get 0.2.
\frac{1}{100.2+0.2}
Add 0.2 and 100 to get 100.2.
\frac{1}{100.4}
Add 100.2 and 0.2 to get 100.4.
\frac{10}{1004}
Expand \frac{1}{100.4} by multiplying both numerator and the denominator by 10.
\frac{5}{502}
Reduce the fraction \frac{10}{1004} to lowest terms by extracting and canceling out 2.