To find the correct option we need to calculate each of the given options.
Option (1):
[tex] \frac{x+2}{x-3} / \frac{4}{x+2} = \frac{x+2}{x-3} * \frac{x+2}{4} = \frac{(x+2)^2}{4(x-3)} [/tex]
Option (2):
[tex] \frac{x+2}{x-3} * \frac{4}{x+2} = \frac{4}{x-3} [/tex]
Option (3):
[tex]\frac{x+2}{x-3} - \frac{4}{x+2} = \frac{(x+2)^2-4(x-3)}{(x-3)(x+2)}[/tex]
option (4)
[tex]\frac{x+2}{x-3} + \frac{4}{x+2} = \frac{(x+2)^2+4(x-3)}{(x-3)(x+2)}[/tex]
So, the correct answer is option (2)
