Question 443815
seven divided by the difference of a number and 2, minus 6 divided by a number plus 2, equals 6 times the reciprocal of the difference of the number squared, and 4, 
:
{{{7/(x-2)}}} - {{{6/(x+2)}}} = {{{6/(x^2-4)}}}
Hey! That's what you had, if you had plunged ahead fearlessly, you probably would have gotten it!
:
Factor the diff of squares, the common denominator is (x-2)(x+2)
{{{7/(x-2)}}} - {{{6/(x+2)}}} = {{{6/(x-2)(x+2))}}}
Multiply each term by the common denominator, the results
7(x+2) - 6(x-2) = 6
7x + 14 - 6x + 12 = 6
7x - 6x + 26 = 6
x = 6 - 26
x = -20
:
See if that works
{{{7/(-20-2)}}} - {{{6/(-20+2)}}} = {{{6/(-20^2-4)}}}
{{{7/(-22)}}} - {{{6/(-18)}}} = {{{6/396}}}
Fortunately the common denominator is 396, so we have
{{{-126/396}}} - {{{-132/396}}} = {{{6/396}}}
which is
{{{-126/396}}} + {{{132/396}}} = {{{6/396}}}