Question 501962
Let the numerator = {{{a}}}
Let the denominator =  {{{b}}}
The original fraction is {{{ a/b }}}
given:
(1) {{{ a = b + 3 }}}
(2) {{{ ( a + 3 ) / ( b - 3 ) = 5/2 }}}
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(2) {{{ a + 3 = (5/2)*( b - 3 ) }}}
(2) {{{ 2*( a + 3 ) = 5*( b - 3 ) }}}
(2) {{{ 2a + 6 = 5b - 15 }}}
(2) {{{ 2a - 5b = -21 }}}
and
(1) {{{ a - b = 3 }}}
Multiply both sides of (1) by {{{2}}}
and subtract (1) from (2)
(2) {{{ 2a - 5b = -21 }}}
(1) {{{-2a + 2b = -6 }}
{{{ -3b = -27 }}}
{{{ b = 9 }}}
and, since
(1) {{{ a = b + 3 }}}
(1) {{{ a = 9 + 3 }}}
(1) {{{ a = 12 }}}
The faction is {{{ a/b = 12/9 }}}