Answer:
The answer is option 2.
Step-by-step explanation:
Firstly, you must factorize the possible expressions :
[tex] \frac{ {x}^{2} - 2x - 15 }{x - 3} \div \frac{x - 5}{ {x}^{2} - 9 } [/tex]
[tex] = \frac{(x - 5)(x + 3)}{x - 3} \div \frac{x - 5}{(x - 3)(x + 3)} [/tex]
Next you have to divide by converting to multiplication :
[tex] = \frac{(x - 5)(x + 3)}{x - 3} \times \frac{(x - 3)(x + 3)}{x - 5} [/tex]
Lastly, you can cut out the similar expressions :
[tex] = \frac{(x - 5)(x + 3)(x - 3)(x + 3)}{(x - 3)(x - 5)} [/tex]
[tex] = {(x + 3)}^{2} [/tex]
