Efetuadas as operações obteve-se [tex]\ [x - 2] / \ [x + 2]\\[/tex].

Para efetuar esta expressão, inicialmente calcula-se o mínimo múltiplo

comum.

[tex](x + 1) / (x - 2) + (2 - 7x) / (x^2 - 4)\\\\MMC = (x+2).( x- 2)\\\\\ [(x + 1).(x + 2) + (2 - 7x)] / (x + 2).(x- 2)\\\\\ [x^2 + 2x + x + 2 + 2 - 7x] / (x + 2).(x - 2)\\\\\ [x^2 - 4x + 4] / (x + 2).(x - 2)\\\\\ [x -2]^2 / (x + 2).(x - 2)\\\\\ [x - 2] / [x + 2]\\\\[/tex]

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[tex]\large\sf{} \dfrac{x + 1}{x - 2} + \dfrac{2 - 7x}{ {x}^{2} - 4 } \\ \\ \large\sf{} \dfrac{x + 1}{x - 2} + \dfrac{2 - 7x}{\left(x - 2\right) \times \left(x + 2\right)} \\ \\ \large\sf{} \dfrac{\left(x + 2\right) \times\left(x + 1\right) + 2 - 7x}{\left(x - 2\right) \times\left(x + 2\right) } \\ \\ \large\sf{} \dfrac{ {x}^{2} + x + 2x + 2 + 2 - 7x}{\left(x - 2\right) \times \left(x + 2\right)} \\ \\ \large\sf{} \dfrac{ {x}^{2} - 4x + 4 }{\left(x - 2\right) \times\left(x + 2\right) } \\ \\\large\sf{} \dfrac{\left(x - 2\right)^{2} }{\left(x - 2\right) \times\left(x + 2\right) } \\ \\ \large\sf{} \dfrac{\cancel{\left(x - 2\right)^{2} }}{\cancel{\left(x - 2\right) } \times\left(x + 2\right) } \\ \\ {\large\boxed{\boxed{  { \large \sf \dfrac{x - 2}{x + 2} }}}}[/tex]

[tex]{\large\boxed{\boxed{  { \large \sf Bons~Estudos }}}}[/tex]