Please solve this question...

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x = 32.123456789123456789....
10^9 * x  = 32123456789.123456789....  # we multiply by 10^9  in order to get the repeated part before the decimal point
thus 10^9 *x -x =   32123456789.123456789.... -  32.123456789123456789....
x(10^9 -1 ) = ( 32123456789 - 32) # since 123456789123456789 after the decimal point is repeated when we delete x from 10^9 * x the value after decimal is removed)
x =   ( 32123456789 - 32) / ( 10^9 - 1 )  
  = 32123456757 / 999,999,999
which is a rational number
 
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