Question 1046192
Let the fraction be {{{ a/b }}}
(1) {{{ b = a + 4 }}}
(2) {{{ ( a + 2 ) / ( b + 2 ) = 3/5 }}}
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Plug (1) into (2)
(2) {{{ ( a + 2 ) / ( a + 4 + 2 ) = 3/5 }}}
(2) {{{ ( a + 2 ) / ( a + 6 ) = 3/5 }}}
Multiply both sides by {{{ 5*( a + 6 ) }}}
(2) {{{ 5*( a + 2 ) = 3*( a + 6 ) }}}
(2) {{{ 5a + 10 = 3a + 18 }}}
(2) {{{ 2a = 8 }}}
(2) {{{ a = 4 }}}
and
(1) {{{ b = a + 4 }}}
(1) {{{ b = 4 + 4 }}}
(1) {{{ b = 8 }}}
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The original fraction is {{{ 4/8 }}}
check:
(2) {{{ ( a + 2 ) / ( b + 2 ) = 3/5 }}}
(2) {{{ ( 4 + 2 ) / ( 8 + 2 ) = 3/5 }}}
(2) {{{ 6/10 = 3/5 }}}
(2) {{{ 3/5 = 3/5 }}}
OK