Question 1084643
<pre>
{{{(x^""-a)/(a^""-b) - (x^""+b)/(a^""+b)}}}{{{""=""}}}{{{(2a(x-b)^"")/(a^2-b^2) + (a^""-b)/(a^""+b)}}}

Factor aČ-bČ

{{{(x-a)/(a-b) - (x+b)/(a+b)}}}{{{""=""}}}{{{(2a(x-b))/((a-b)(a+b)) + (a-b)/(a+b)}}}

To avoid denominators equaling 0, we must have the restrictions
that a &#8800; b and a &#8800; -b

Multiply through by LCD of (a-b)(a+b)

{{{(x-a)(a+b) - (x+b)(a-b)}}}{{{""=""}}}{{{2a(x-b) + (a-b)(a-b)}}}

{{{(ax+bx-a^2-ab) - (ax-bx+ab-b^2))}}}{{{""=""}}}{{{2ax-2ab + (a^2-ab-ab+b^2)}}}

{{{ax+bx-a^2-ab - ax+bx-ab+b^2}}}{{{""=""}}}{{{2ax-2ab + a^2-ab-ab+b^2}}}

{{{-a^2 + b^2 + 2bx}}}{{{""=""}}}{{{a^2 - 4ab + 2ax + b^2}}} 

{{{-2ax + 2bx}}}{{{""=""}}}{{{2a^2 - 2ab}}}

Divide through by -2

{{{ax - bx}}}{{{""=""}}}{{{-a^2 + ab}}}

{{{x(a - b)}}}{{{""=""}}}{{{-a(a - b)}}}

{{{x}}}{{{""=""}}}{{{-a(a - b)/(a-b)}}}

{{{x}}}{{{""=""}}}{{{(-a(cross(a-b) ))/( cross(a-b) )}}}

{{{x}}}{{{""=""}}}{{{-a}}}

Edwin</pre>