Are these problems right?

Question

I am trying to find the tangent slope of this one, so essentially just simplifying as much as possible 

(sqrt(x) - 2) / (x - 4) 

my answer: 1/(sqrt(x) + 2x -8) 

and 

Find the vertical asymptotes of the graph of f(x): (x^2 - 4) / (x^3 + 2x^2 + x + 2) 

My answer: none

Answer 1

2) The rational function

Simplify the rational function.

Apply the formula difference of two squares

vertical asymptotes are found  by solving denominator = 0.

In this case roots are imaginary.

Therefore, there is no vertical asymptotes.

Your answer is correct.

Answer 2

1) The function 

Simplify the function.

Derivative of the function is the slope of the tangent .

Apply derivative on each side with respect of x.

Apply quotient rule in derivatives

Your answer is wrong.