Question 581781
The sum of the reciprocals of two numbers is 3/2, and the difference of their reciprocals is 5/12. 
what are the two numbers
:
{{{1/a}}} + {{{1/b}}} = {{{3/2}}}
{{{1/a}}} + {{{1/b}}} = {{{18/12}}}
and
{{{1/a}}} - {{{1/b}}} = {{{5/12}}}
-------------------------adding eliminates b, find a
{{{2/a}}} = {{{23/12}}}
Cross multiply
23a = 2*12
23a = 24
a = {{{24/23}}}
Find b
{{{23/24}}} + {{{1/b}}} = {{{3/2}}}
{{{1/b}}} = {{{3/2}}} - {{{23/24}}}
{{{1/b}}} = {{{36/24}}} - {{{23/24}}}
{{{1/b}}} = {{{13/24}}}
cross multiply
13b = 24
b = {{{24/13}}}
:
:
Check this in the 2nd original equation
{{{23/24}}} - {{{13/24}}} = {{{10/24}}} = {{{5/12}}}