Determine the rational number that becomes if 1 is subtracted from its numerator and denominator, and it becomes
if 7 is added to its denominator.
Let the rational number be denoted by . Then, from
the information in the question, we can conclude that
Multiplying by gives
Also from information given in the question, we conclude that
This pair of equations can now be solved using the omitting
method. Multiplying the first equation by 9 gives
Multiplying the second equation by 4 gives
Subtracting the equations gives
Substituting this value of into the first equation gives
Therefore, the rational number is
which can be simplified to .