SOLUTION: find asymptotes and holes for (x+4)(x-2) all over (x-6)(x-2) and graph {{{(x+4)(x-2)/((x-6)(x-2))}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: find asymptotes and holes for (x+4)(x-2) all over (x-6)(x-2) and graph {{{(x+4)(x-2)/((x-6)(x-2))}}}      Log On


   

Question 741841: find asymptotes and holes for (x+4)(x-2) all over (x-6)(x-2)
and graph
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Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
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Vertical asymptote at x=6, because that would be where the function is undefined due to x-6 being in the denominator as a factor. Division by zero is impossible.
A hole is at x=2, because the binomial factor, x-2 is a factor in both the numerator and the denominator, giving the expression (x-2)/(x-2), which is 1; yet this expression IS still part of the rational expression given, and with x-2 in the denominator, x cannot be +2, since this would create a division by 0 when x=2.

Please note here, the hole at x=2 is not appearing properly:
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