SOLUTION: Can you tell me if this answer is correct? Determine the vertical asympotes for the function f(x)= {{{(x^2-16)/(3x^2-3)}}} My answer: {{{x=0}}}, {{{x=sqrt(1)}}}, {{{x= -

Can you tell me if this answer is correct?
Determine the vertical asympotes for the function 



My answer:

, , 

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The  is incorrect!  The other two are correct
except that you would never leave those answers
unsimplified as  and 

Since , the answers should be 
simplified as:

 and 

You simply set the denominator of



equal to 0



Divide every term on both sides through by 3





There are two ways to solve that:

1. Factor the left side as the difference
of squares:



Set each factor = 0

Setting the first factor = 0,





Setting the second factor = 0,



 

2. The way you apparently did it:


 
Add + to both sides



Take square roots of both sides

 and 

which simplifies to

 and 

That is perfectly OK.

[But there is no way you could have 
gotten !]

Let's look at the graph of 





Now let's draw in the two vertical 
asymptotes at x=-1 and a=1:



and you can see that the curve approches 
those two asymptotes on both sides. The
curve gets closer and closer to these 
asymptotes but never touches them! 

Edwin