Question

(X+2)/ (x _2) + (x_2)/( x+2)

Answer 1

Answer:

$\frac{2 {x}^{2} + 8 }{ {x}^{2} - 4}$

Step-by-step explanation:

$= > \frac{( x + 2)}{(x - 2)} + \frac{(x - 2)}{(x + 2)} \\ \\ \bigstar \: take \: lcm \: (x - 2)(x + 2) \\ \\ = > \frac{ {(x + 2)}^{2} }{(x - 2)(x + 2)} + \frac{ {(x - 2)}^{2} }{(x - 2)(x + 2)} \\ \\ = > \frac{ {x}^{2} + 4x + 4 }{ {x}^{2} - 4 } + \frac{ {x}^{2} - 4x + 4}{ {x}^{2} - 4 } \\ \\ = > \frac{ {x}^{2} + {x}^{2} + 4x - 4x + 4 + 4}{ {x}^{2} - 4 } \\ \\ = > \frac{2 {x}^{2} + 8 }{ {x}^{2} - 4}$