Question 921311

start with {{{a/b}}}

twice the numerator ({{{2a}}}) is {{{2}}} more than the denominator ( {{{b}}}): 

{{{2a=b+2}}} =>{{{a=b/2+1}}}

  the new fraction is   {{{a/b=(b/2+1)/b}}}

{{{3}}} is added to each

{{{((b/2+1)+3)/(b+3)}}} and it is equal to {{{2/3}}}

{{{((b/2+1)+3)/(b+3) =2/3}}} .........solve for {{{b}}}

{{{(b/2+4)/(b+3) =2/3 }}}

{{{3(b/2+4) =2(b+3)}}}

{{{3b/2+12 =2b+6}}}

{{{12-6 =2b-3b/2}}}

{{{6=4b/2-3b/2}}}

{{{6 =b/2}}}

{{{6*2 =b}}}

{{{12=b}}}

=>{{{a=b/2+1}}} => {{{a=12/2+1}}} => {{{a=6+1}}}=>{{{a=7}}}

original fraction is: {{{a/b=7/12}}}