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? 
:
{{{6/((x-2)) - 5/((x+2)) = 5(1/((x^2-4)))}}}
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/((-17-2)) - 5/((-17+2)) = 5(1/((-17^2-4)))}}}
{{{6/(-19) - 5/(-15) = 5(1/(289-4))}}}
{{{-6/19 + 5/15 = 5/285}}} Checks out on a my calc