SOLUTION: The sum of the reciprocals of two numbers is 3/2, and the difference of their rciprocals is 5/12. what are the two numbers

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Question 581781: The sum of the reciprocals of two numbers is 3/2, and the difference of their rciprocals is 5/12. what are the two numbers
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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%2Fa + 1%2Fb = 3%2F2
1%2Fa + 1%2Fb = 18%2F12
and
1%2Fa - 1%2Fb = 5%2F12
-------------------------adding eliminates b, find a
2%2Fa = 23%2F12
Cross multiply
23a = 2*12
23a = 24
a = 24%2F23
Find b
23%2F24 + 1%2Fb = 3%2F2
1%2Fb = 3%2F2 - 23%2F24
1%2Fb = 36%2F24 - 23%2F24
1%2Fb = 13%2F24
cross multiply
13b = 24
b = 24%2F13
:
:
Check this in the 2nd original equation
23%2F24 - 13%2F24 = 10%2F24 = 5%2F12