Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ \frac{4x}{(x + 2)(x - 2)}}}}}} [/tex]
Step-by-step explanation:
[tex] \sf{ \frac{1}{x + 2} + \frac{1}{x - 2} + \frac{2x}{ {x}^{2} + 4} }[/tex]
Use the formula of a² - b² = ( a + b ) ( a - b )
[tex] \longrightarrow{ \sf{ \frac{1}{x + 2} + \frac{1}{x - 2} + \frac{2x}{ {x}^{2} + {2}^{2} } }}[/tex]
[tex] \longrightarrow{ \sf{ \frac{1}{x + 2} + \frac{1}{x - 2} + \frac{2x}{(x + 2)(x - 2)}}} [/tex]
[tex] \longrightarrow{ \sf{ \frac{x - \cancel{2} + x + \cancel{ 2} + 2x}{(x + 2)(x -2 )} }}[/tex]
[tex] \longrightarrow{ \sf{ \frac{4x}{(x + 2)(x - 2)}} } [/tex]
Hope I helped!
Best regards! :D
