Question 1156497
The sum of the reciprocals of 2 consecutive odd integers is 8/15. Find the numbers.
<pre>Let the smaller odd integer be N
Then the larger odd integer = N + 2
We then get: {{{matrix(1,3, 1/N + 1/(N + 2), "=", 8/15)}}}
15(N + 2) + 15N, "=", 8N(N + 2) ------ Multiplying by LCD, 15N(N + 2)
{{{matrix(1,3, 15N + 30 + 15N, "=", 8N^2 + 16N)}}}
{{{matrix(1,3, 30N + 30, "=", 8N^2 + 16N)}}}
{{{matrix(4,3, 8N^2 + 16N - 30N - 30, "=", 0,
8N^2 - 14N - 30, "=", 0,
2(4N^2 - 7N - 15), "=", 2(0),
4N^2 - 7N - 15, "=", 0)}}}
{{{matrix(1,3, 4N^2 - 12N + 5N - 15, "=", 0)}}} ------ Replacing - 7N with - 12N + 5N
4N(N - 3) + 5(N - 3) = 0
(N - 3)(4N + 5) = 0
N, or smaller odd integer = {{{highlight_green(3)}}}             or           {{{matrix(1,4, N, "=", - 5/4, "(ignore)")}}}
Do you know what the larger odd integer is now?