To find the asymptotes, we have to solve the following.
[tex]x^2-4x+3=0[/tex]
We have to find two numbers whose product is 3 and whose sum is 4. Those numbers are 3 and 1.
[tex](x-3)(x-1)=0[/tex]
So, the solutions are x = 3 and x = 1.
Hence, the asymptotes x = 1 and y = 1/2.
The graph below shows the function.
