Question

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Answer 1

The answer is the third one, C

Answer 2

The correct answer is:  [C]:  $\frac{3x}{x-5}$ ; x ≠ 5, x ≠ -3 .
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Explanation:
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We are given the following expression:
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$\frac{3 x^{2} + 9x}{ x^{2} -2x-15}$ ;
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  We can factor the "denominator" as follows:
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  The denominator:   " x² − 2x − 15 " ; can be factored into: 
         →  " (x−5)(x+3) " ;
         →To solve this problem, we want to see if we can factor the number into one of the factors of the denominator; that way we can ultimately "cancel out" one of the same "factors" in both the numerator AND the denominator; (since "any value", divided by that "same value",  equals "1".  The purpose  is to see if we can further simplify the expression (ultimately).
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  → In our case, we can do so; 
   → We can factor out the "numerator" — as follows:
→ The numerator:  " 3x² + 9x " ; can be "factored out", into:  "(3x)(x+3)" ;

 →  Now, we have:"(x+3)" in BOTH the numerator AND the denominator).
→   So, we can rewrite the expression as:
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   $\frac{(3x)(x+3)}{(x-5)(x+3)}$   ;
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At this point, examine the denominator:  → "(x−5)(x+3)" .
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 Note: The "denominator" cannot equal "0" ; since we cannot "divide by zero".
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      So the restrictions on the value for "x" are:  {"any values for "x" in the denominator; that would make the denominator equal to "0" (zero)".}.
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        Note that any value, when multiplied by "0" (zero), will result  in a product [value] of "0" (zero).
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  So; we can see that in the [factored] denominator, which is:
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    "(x−5)(x+3)" ;  that there are "2 (TWO) multiplicands" , which are:
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 1)  "(x−5)" ; AND:  2)  "(x+3)" ;