SOLUTION: Six divided by the difference of a number and 2,minus 5 divided by a number plus 2, equals 2 times the reciprocal of the difference of the number squared and 4. What is the​

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Question 1080276: Six divided by the difference of a number and 2,minus 5 divided by a number plus 2, equals 2 times the reciprocal of the difference of the number squared and 4. What is the​ number?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
6/(n-2),
.
.
(6/(n-2))-5/(n+2),
.

%286%2F%28n-2%29%29-5%2F%28n%2B2%29=2%281%2F%28n%5E2-4%29%29

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6%2F%28n-2%29-5%2F%28n%2B2%29=2%2F%28n%5E2-4%29

Multiply both sides by simplest common denominator %28n-2%29%28n%2B2%29=n%5E2-4;

6%28n%2B2%29-5%28n-2%29=2
6n%2B12-5n%2B10=2
n=2-12-10
highlight%28n=-20%29,








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check
6/(-20-2)-5/(-20+2)=2/((-20)^2-4)
6/(-22)-5/(-18)=2/(400-4)
-3/11+5/18=2/396
5/18-3/11=1/198
LCD 198
.
0.005050505 and 0.0050505050