if $x\ll 1$ is it safe to assume that $x\ll \frac{1}{2}$

Question

I know that:

if $x\ll 1$ then we can write $\frac{x}{x+1}\rightarrow x$

but is it safe to write $\frac{2x+1}{x+1}\rightarrow 1$?

Answer 1

$\dfrac{2x+1}{x+1} = 2 - \dfrac{1}{1+x} \approx 2 - (1-x)=1+x$