How do you find the vertical, horizontal or slant asymptotes for #y=(2x)/(x-3)#?

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Answer 1 · 2016-11-07T10:52:30

#color(blue)(x=3)# is a Vertical Asymptote.

#color(blue)(y=2)# is the Horizontal Asymptote.

#No Slant Asymptote#

Vertical Asymptote is determined by setting the denominator to zero :

#x-3=0rArrx=3#
Therefore ,

#color(blue)(x=3)# is a Vertical Asymptote.

The degree of the numerator is the same as that of the denominator , so there is Horizontal Asymptote but no slant Asymptote .

If the numerator and denominator have the same degree

#(a x^ n +b x +c )/(a 'x ^n + b')#

Then the Horizontal Asymptote is , #a/(a')" #,the fraction formed by their coefficients of the highest degree.

In the given quotient ,the numerator and denominator have the same degree #1# ,

therefore,

#color(blue)(y=2)# is the Horizontal Asymptote.