What are the asymptotes for #(x-3) / (x-2) #?

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Answer 1 · 2015-08-08T01:52:18

There is a vertical asymptote at #color(red)(x=2)# and a horizontal asymptote at #color(red)(y=1)#.

#y=(x-3)/(x-2)#

Step 1. Find the vertical asymptotes.

Set the denominator equal to zero and solve for #x#.

#x-2=0#

#x=2#

There is a vertical asymptote at #x=2#.

Step 2. Find the horizontal asymptotes.

We divide the coefficients of the highest terms.

#1/1=1#

The horizontal asymptote is at #y=1#.

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