Question 119283
Let's say that your original fraction is {{{p/q}}}.  And we know that {{{q=3p}}}, so we can re-write the original fraction as {{{p/3p}}}.


If we add 1 to the numerator and subtract 1 from the denominator, we get:


{{{(p+1)/(3p-1)}}}  which we are told is equal to {{{1/2}}}, so


{{{(p+1)/(3p-1)=1/2}}}.  This is an equation in a single variable that can be solved by ordinary methods.


Step 1: Cross-multiply.
{{{2(p+1)=(3p-1)}}}


Step 2: Distribute the 2 on the left
{{{2p+2=3p-1}}}


Step 3: Add -3p to both sides
{{{2p-3p+2=-1}}}


Step 4: Add -2 to both sides
{{{2p-3p=-1-2}}}


Step 5: Collect like terms:
{{{-p=-3}}}


Step 6: Multiply both sides by -1
{{{p=3}}}, giving us the numerator of the original fraction.


If the numerator of the original fraction is 3, the denominator is {{{3*3=9}}}, hence the original fraction must have been {{{3/9}}}


Check:
{{{(3+1)/(9-1)=4/8=1/2}}}


Hope this helps,
John