Question 821765
Let:
x - 1st positive integer
y - 2nd positive integer
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{{{xy=8}}} eq 1
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{{{x+y=6}}}eq 2
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Solution:
-formulate eq 1
{{{x=8/y}}}eq3
-then subtitute eq 3 to eq 2
{{{(8/y)+y=6}}}
-multiply both sides by y
{{{8+y^2=6y}}}
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{{{y^2-6y+8=0}}}
-factor
{{{(y-2)(y-4)=0}}}
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{{{highlight(y=2)}}} 
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reciprocal{{{highlight(y=1/2)}}}
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{{{x=8/2}}}
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{{{highlight (x=4)}}}
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reciprocal{{{highlight (x=1/4)}}}
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sum of their reciprocal
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{{{1/2+1/4)}}} LCD=4
{{{(2+1)/4)}}}
={{{highlight (3/4))}}}