Question 73281
.
{{{(1-(2/(x+2)))/(1+(2/(x-2)))}}}
.
This is how I interpreted your problem and I hope that is correct.
.
In the numerator let's put everything over the common denominator of (x+2).  We can do that 
by replacing the 1 with {{{(x+2)/(x+2)}}} and this will make the numerator:
.
{{{((x+2)/(x+2))-(2/(x+2)))}}}
.
and when you combine this numerator over its common denominator the result is:
.
{{{(x+2 -2)/(x+2)}}}
.
and this further simplifies to:
.
{{{(x)/(x+2)}}}
.
Next we'll do the same thing to the denominator.

In the denominator let's put everything over the common denominator of (x-2).  We can do that 
by replacing the 1 with {{{(x-2)/(x-2)}}} and this will make the denominator become:
.
{{{((x-2)/(x-2))+(2/(x-2)))}}}
.
and when you combine this over its common denominator the result is:
.
{{{(x-2 +2)/(x-2)}}}
.
and this further simplifies to:
.
{{{(x)/(x-2)}}}
.
Now, putting the numerator and denominator back together in their new forms we get:
.
{{{((x)/(x+2))/((x)/(x-2)))}}}
.
The rule for dividing by a fraction (the denominator) is to invert it and multiply it
times the number being divided. We can apply that rule here and get:
.
{{{((x)/(x+2))*((x-2)/x)}}}
.
which when multiplied becomes
.
{{{(x*(x-2))/(x*(x+2))}}}
.
canceling the x in the denominator with the x in the numerator finally gets us to the answer:
.
{{{(x-2)/(x+2)}}}
.
Hope I interpreted your problem correctly and this is the work you were looking for.