Question 921358

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The sum of reciprocals of two consecutive even integers is 7/24. Find each integer
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Let smaller integer be S
Then larger = S + 2
Therefore, {{{1/S + 1/(S + 2) = 7/24}}}
24(S + 2) + 24S = 7(S)(S + 2) ------- Multiplying by LCD, 24S(S + 2)
{{{24S + 48 + 24S = 7S^2 + 14S}}}
{{{48S + 48 = 7S^2 + 14S}}}
{{{7S^2 + 14S - 48S - 48 = 0}}}
{{{7S^2 - 34S - 48 = 0}}}
(S - 6)(7S + 8) = 0 
S, or smaller integer = {{{highlight_green(6)}}}		OR		S = - 8/7 (ignore)
Larger integer: 6 + 2, or {{{highlight_green(8)}}}
You can do the check!! 
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