SOLUTION: I need help finding 2 consecutive natural numbers such that the difference of their reciprocals is 1/4 the reciprocal of the smaller number.

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Question 544837: I need help finding 2 consecutive natural numbers such that the difference of their reciprocals is 1/4 the reciprocal of the smaller number.
Answer by friesr(113) About Me  (Show Source):
You can put this solution on YOUR website!
x
x + 1 =
1%2F%28x%2B1%29-+1%2Fx+=+1%2Fx+%2A+1%2F4
Lets get a commone denominator:
+x%2F%28x%28x%2B1%29%29+-+%28x%2B1%29%2F%28x%28x%2B1%29%29+=+1%2F4x
-
+x-x%2B1+%2F+x%28x%2B1%29+=+1%2F4x
-
1%2Fx%28x%2B1%29+=+1%2F%284x%29
-
Multiply both sides by x
1%2F%28x%2B1%29+=+1%2F4
-
x%2B1+=+4
--
x=3
===
Your numbers are 3 and 4
--
Check:
1/3 - 1/4 = 1/4 * 1/3
-
4/12 - 3/12 = 1/12
1/12 = 1/12