Question 1048318
{{{ 1/8= 1/A + 1/B }}}  ===> {{{1/8 - 1/A = 1/B}}}

===> {{{B = (8A)/(A-8)}}}  ===>  {{{B = 8(1+8/(A-8))}}}

===> A - 8 must divide 8

===> A - 8 = 1, 2, 4, 8.

===> A = 9, 10, 12, 16

If A = 9, B = 72,
If A = 10, B = 40,
If A = 12, B = 24,
If A = 16, B = 16.

Eliminate the last possibility. (Why?)

Hence there are three possible values of A+B, namely 81, 50, and 36.

Now you can do the same for 1/9 and 1/10 also.