Question 184309
I think you had a typo in your expression.  I think you meant:
{{{    ((x+2)/4) * (2/(x^2-4)) }}}
.
If so, factor the denominator to get:
{{{    ((x+2)/4) * (2/((x-2)(x+2))) }}}
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Notice the (x+2) cancel leaving:
{{{    (1/4) * (2/(x-2)) }}}
.
Now, we can reduce the 2 and 4:

{{{    (1/2) * (1/(x-2)) }}}
.
Resulting in:
{{{ 1/(2(x-2)) }}}