Given:
[tex]\frac{x+2}{x^2-4x+4}[/tex]
To simplify the given rational expression, we first factor x^2-4x+4 by applying Perfect Square Formula as shown below:
[tex]\begin{gathered} a^2-2ab+b^2=(a-b)^2 \\ \end{gathered}[/tex]
Hence,
[tex]x^2-4x+4=x^2-2x(2)+2^2=(x-2)^2[/tex]
Now, we simplify the given expression:
[tex]\frac{x+2}{x^{2}-4x+4}=\frac{x+2}{(x-2)^2}[/tex]
Therefore, the answer is:
[tex]\frac{x+2}{(x-2)^{2}}[/tex]
