Rewrite \({x}^{2}-4\) in the form \({a}^{2}-{b}^{2}\), where \(a=x\) and \(b=2\).
\[\frac{3}{{x}^{2}-{2}^{2}}+\frac{1}{{(x-2)}^{2}}\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[\frac{3}{(x+2)(x-2)}+\frac{1}{{(x-2)}^{2}}\]
Rewrite the expression with a common denominator.
\[\frac{3(x-2)+x+2}{(x+2){(x-2)}^{2}}\]
Expand.
\[\frac{3x-6+x+2}{(x+2){(x-2)}^{2}}\]
Collect like terms.
\[\frac{(3x+x)+(-6+2)}{(x+2){(x-2)}^{2}}\]
Simplify \((3x+x)+(-6+2)\) to \(4x-4\).
\[\frac{4x-4}{(x+2){(x-2)}^{2}}\]
Factor out the common term \(4\).
\[\frac{4(x-1)}{(x+2){(x-2)}^{2}}\]
(4*(x-1))/((x+2)*(x-2)^2)
