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Please name where the vertical asymptote are as well as any horizontal ones as well. Also write where the removable discontinuities are.

f(x)= (x-2)(x-1) รท (x-2)2(x-1)
 
Please name where the vertical asymptote are as well as any horizontal ones as well. Also write where the removable discontinuities are. 
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1 Answer

There is a vertical asymptote at x=2, a horizontal asymptote at y=0, and a removable discontinuity at x=1.

Comments

But why is there not one a r.d at 2. Wouldn't that make the denominator zero as well?
Yes, there is a discontinuity at x=2, but it isn't removable.  The two x-1 terms cancel (and are thus removed).  You can remove one of the x-2 terms in the denominator but not the other, so the discontinuity remains.
John,
 
As Philip noted, a discontinuity in a function is only removable if the term in the function that caused the discontinuity can be canceled.  Another way to look at it is that a vertical asymptote, such as the one at x=2 in this case, is a discontinuity that cannot be removed.