[tex] \frac{ {x}^{2} - 4 }{ {x}^{2} - 4x + 4} = \frac{ {x}^{2} - {2}^{2} }{ {x}^{2} - 4x + 4 } = \frac{(x + 2)(x - 2)}{ {x}^{2} - 4x + 4 } = \frac{(x + 2)(x - 2) }{ {x}^{2} - 2(x)(2) + {2}^{2} } = \frac{(x + 2)(x - 2)}{ {(x - 2)}^{2} } = \frac{x + 2}{x - 2} [/tex]