Question

Hi, simplify the following rational expression, if possible: x + 2/ x^2 = 4x + 4

Answer 1

Given:

`(x+2)/(x^2-4x+4)`

To simplify the given rational expression, we first factor x^2-4x+4 by applying Perfect Square Formula as shown below:

`\begin{gathered} a^2-2ab+b^2=(a-b)^2 \\ \end{gathered}`

Hence,

`x^2-4x+4=x^2-2x(2)+2^2=(x-2)^2`

Now, we simplify the given expression:

`(x+2)/(x^(2)-4x+4)=(x+2)/((x-2)^2)`

Therefore, the answer is:

`(x+2)/((x-2)^(2))`