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Find the vertical asymptote for y=(x-2)/((x-2)(x+3)).

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Final answer:

The function y=(x-2)/((x-2)(x+3)) simplifies to y=1/(x+3), thus the vertical asymptote is at x=-3, representing the value where the function is undefined due to division by zero.

Step-by-step explanation:

To find the vertical asymptote of the function y=(x-2)/((x-2)(x+3)), we first need to simplify the function. Notice that (x-2) appears in both the numerator and the denominator, so it cancels out, leaving us with y=1/(x+3).

Therefore, the vertical asymptote will occur where the denominator is zero, which happens when x is -3. However, since the x-2 terms cancel out, it is not a vertical asymptote but rather a hole at x=2. Hence, the only vertical asymptote of this simplified function is at x=-3.

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