SOLUTION: 6 divided by the difference of a number and 2​, minus 5 divided by a number plus 2​, equals 5 times the reciprocal of the difference of the number squared and 4. What i

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Question 1075068: 6 divided by the difference of a number and 2​, minus 5 divided by a number plus 2​, equals 5 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!
6 divided by the difference of a number and 2​, minus 5 divided by a number plus 2​, equals 5 times the reciprocal of the difference of the number squared and 4. What is the​ number?
:
6%2F%28%28x-2%29%29+-+5%2F%28%28x%2B2%29%29+=+5%281%2F%28%28x%5E2-4%29%29%29
we know that (x-2)(x+2) = x^2-4
multiply equation by x^2-4, cancel the denominators, then we have
6(x+2) - 5(x-2) = 5
6x + 12 - 5x + 10 = 5
6x - 5x + 22 = 5
x = 5 - 22
x = -17
:
:
See if that checks out
6%2F%28%28-17-2%29%29+-+5%2F%28%28-17%2B2%29%29+=+5%281%2F%28%28-17%5E2-4%29%29%29
6%2F%28-19%29+-+5%2F%28-15%29+=+5%281%2F%28289-4%29%29
-6%2F19+%2B+5%2F15+=+5%2F285 Checks out on a my calc