Range of a rational function with radicals Find the range of the function 
$$\frac{6}{5\sqrt{x^2-10x+29} - 2}$$
I tried using inverses, but the equation got super messy and I dont think its a good method for this problem.
$\frac{6}{5\sqrt{x^2-10x+29} - 2} = y$ 
getting the inverse,
$\frac{6}{5\sqrt{y^2-10y+29} - 2} = x$ 
$\frac{4x^2+24x+36}{25x^2}= y^2-10y +29$
Then it would be a quadratic function in y,  but the discriminant becomes really big
$100- 116(\frac{4x^2+24x+36}{25x^2})$

Hint
If you rewrite $x^2-10x+29=(x-5)^2+4$, it's easier to see that:
$$(x-5)^2+4 \in [4,+\infty)$$
$$\sqrt{(x-5)^2+4}  \in [2,+\infty)$$
$$5\sqrt{(x-5)^2+4}-2  \in [8,+\infty)$$
Does that help?
