Question

select all the correct answers.
for which values is this expression undefined?
\\(\frac{3x}{x^2 - 9} - \frac{x + 4}{x^2 + 2x - 15}\\)
\\(x = -5\\)
\\(x = 0\\)
\\(x = -3\\)
\\(x = -4\\)
\\(x = 5\\)
\\(x = 3\\)

Explanation:

Step1: Factor first denominator

$x^2 - 9 = (x-3)(x+3)$

Step2: Find zeros of first denominator

Set $(x-3)(x+3)=0$
Solutions: $x=3$, $x=-3$

Step3: Factor second denominator

$x^2 + 2x -15 = (x+5)(x-3)$

Step4: Find zeros of second denominator

Set $(x+5)(x-3)=0$
Solutions: $x=-5$, $x=3$

Step5: Collect all undefined values

Combine unique zeros: $x=-5, x=-3, x=3$

Answer:

$x = -5$, $x = -3$, $x = 3$