Question 624877
Let the fraction = {{{ a/b }}}
given:
(1) {{{ a + b =  11 }}}
(2) {{{ ( a + 1 ) / ( b - 2 ) = 2/3 }}}
----------------------------
Multiply both sides of (2) by {{{ 3*( b - 2 ) }}}
(2) {{{ 3*( a + 1 )  = 2*( b - 2 ) }}}
(2) {{{ 3a + 3 = 2b - 4 }}}
(2) {{{ 3a - 2b = -7 }}}
------------------
Multiply both sides of (1) by {{{ 2 }}}
and add the equations
(1) {{{ 2a + 2b =  22 }}}
(2) {{{ 3a - 2b = -7 }}}
{{{ 5a = 15 }}}
{{{ a = 3 }}}
and, since
(1) {{{ a + b =  11 }}}
(1) {{{ 3 + b =  11 }}}
(1) {{{ b = 8 }}}
The fraction is 3/8
check:
(2) {{{ ( a + 1 ) / ( b - 2 ) = 2/3 }}}
(2) {{{ ( 3 + 1 ) / ( 8 - 2 ) = 2/3 }}}
(2) {{{ 4/6 = 2/3 }}}
(2) {{{ 2/3 = 2/3 }}}
OK