Question 1192891
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Your statement of the problem is not clear.  When the problem says the fraction is "increased by 1/12", it is not clear whether that is an increase by a FACTOR of 1/12 or an increase of an ADDED 1/12.<br>
The other tutor interpreted the meaning to be an increase by a factor of 1/12, which makes the problem have no solution.<br>
The problem has a solution if the increase is an added 1/12.<br>
Let the denominator of the original fraction be x; then the two fractions are (x-1)/x and (x+1)/(x+2).<br>
The second fraction is 1/12 MORE than the first:<br>
{{{(x+1)/(x+2)-(x-1)/x=1/12}}}
{{{(x+1)(x)-(x-1)(x+2)=(x(x+2))/12}}}
{{{(x^2+x)-(x^2+x-2)=(x^2+2x)/12}}}
{{{2=(x^2+2x)/12}}}
{{{x^2+2x=24}}}
{{{x^2+2x-24=0}}}
{{{(x+6)(x-4)=0}}}<br>
{{{x=-6}}} or {{{x=4}}}<br>
If we choose the positive solution, then the original fraction is 3/4 and the new fraction is 5/6, and 5/6 - 3/4 = 10/12 - 9/12 = 1/12; the conditions of the problem are satisfied.<br>
If we choose the negative solution, the the original fraction is (-7)/(-6) and the new fraction is (-5)/(-4); and (-5)/(-4) - (-7)/(-6) = 5/4 - 7/6 = 15/12 = 14/12 = 1/12; again the conditions of the problem are satisfied.<br>
So the original fraction could be either 3/4 or (-7)/(-6).  However, the format of the second "solution" is not standard, so....<br>
ANSWER: The original fraction was 3/4<br>