Question 691741
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/((n-2))}}} - {{{8/((n+2))}}} =  6*{{{1/((n^2-4))}}}
Factor the the 3rd denominator
{{{9/((n-2))}}} - {{{8/((n+2))}}} =  6*{{{1/((n-2)(n+2))}}}
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
:
:
See if that works
{{{9/((-28-2))}}} - {{{8/((-28+2))}}} =  6*{{{1/((-28^2-4))}}}
using a calc
{{{9/(-30)}}} - {{{8/(-26)}}} =  6*{{{1/((784-4))}}}
-.3 - (-.3077) = .0077
-.3 + .3077) = .0077