Question 969596
Horizontal Asymptote:  Degree of numerator equals degree of denominator.


Vertical Asymptote x=2:  {{{something/(x-2)}}}


x-intercept -1:   {{{(something(x+1))/(x-2)}}}


Hole and undefined at x=1:   {{{((x+1)(x-1))/((x-2)(x-1))}}}


Almost finished.  You want horizontal asymptote y=5.  Leading terms must become increasingly large and positive as x goes to the right or left unbounded and ratio must approach 5.


{{{highlight((5(x+1)(x-1))/((x-2)(x-1)))}}}
and you can multiply fully if desired.



{{{graph(400,400,-10,10,-30,30,(5(x+1)(x-1))/((x-2)(x-1)))}}}