SOLUTION: nine divided by the difference of a number and 2 minus 8 divided by a number plus 2, equals 6 times the reciprocal of the difference of the number squared and 4. What is the number

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Question 691741: nine divided by the difference of a number and 2 minus 8 divided by a number plus 2, equals 6 times the reciprocal of the difference of the number squared and 4. What is the number?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Write an equation for just what it says:
:
nine divided by the difference of a number and 2 minus 8 divided by a number plus 2, equals 6 times the reciprocal of the difference of the number squared and 4.
9%2F%28%28n-2%29%29 - 8%2F%28%28n%2B2%29%29 = 6*1%2F%28%28n%5E2-4%29%29
Factor the the 3rd denominator
9%2F%28%28n-2%29%29 - 8%2F%28%28n%2B2%29%29 = 6*1%2F%28%28n-2%29%28n%2B2%29%29
Multiply thru by the common denominator, cancel the denominators, results:
9(n+2) - 8(n-2) = 6
9n + 18 - 8n + 16 = 6
9n - 8n = 6 - 34
n = -28 is the number
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See if that works
9%2F%28%28-28-2%29%29 - 8%2F%28%28-28%2B2%29%29 = 6*1%2F%28%28-28%5E2-4%29%29
using a calc
9%2F%28-30%29 - 8%2F%28-26%29 = 6*1%2F%28%28784-4%29%29
-.3 - (-.3077) = .0077
-.3 + .3077) = .0077