Show $2 \lt f(x) \lt 2.8$? I have a question about a function $f(x)$:
$$f(x) = -x + \frac{x^2}{x-2} - \frac{20}{x^2 + x - 6},\qquad x>2$$
simplifies to
$$f(x) = 2x + \frac{10}{x + 3},\qquad x>2$$
How would you show the range of $f(x)$ is $2 < f(x) < 2.8?$
Thank you.

I think it should be $$\frac{2x+10}{x+3}=\frac{2(x+3)+4}{x+3}=2+\frac4{x+3}$$
As $\displaystyle x>2,x+3>5\implies0<\frac1{x+3}<\frac15$
