Remove asymptote of a function

I'm trying to draw the functions y=(0.05*0.4+0.1*2*x)/(0.05+0.1*2) and x=-0.1/(2*30*(y - 0.1))+y, by using tikz as follows

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}
\begin{axis}[xmin=0,xmax=1,ymin=0,ymax=1, samples=1000, xlabel={$c$}, ylabel={$s$}]
\addplot[blue, ultra thick] (x,{(0.05*0.4+0.1*2*x)/(0.05+0.1*2)});
\addplot[red,  ultra thick] ({-0.1/(2*30*(x - 0.1))+x},x);
\end{axis}
\end{tikzpicture}
\end{document}


and the result is

Thanks to the answers to Tikz picture of two mathematical functions, I was able to draw the functions correctly. However, I notice (red) the presence of an asymptote which should be traced or removed (it is not part of fraph of a function).

It's not an asymptote, it's a straight line between 2 plots, because of a discontinuity: the graph defined by x=-0.1/(2*30*(y - 0.1))+y has discontinuity at y=0.1.

You can remedy so:

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}
\begin{axis}[xmin=0,xmax=1,ymin=0,ymax=1, samples=1000, xlabel={$c$}, ylabel={$s$}]
\addplot[blue, ultra thick] (x,{(0.05*0.4+0.1*2*x)/(0.05+0.1*2)});
\addplot[red,  ultra thick, domain=0:0.0999] ({-0.1/(2*30*(x - 0.1))+x},x);
\addplot[red,  ultra thick, domain=0.1001:1] ({-0.1/(2*30*(x - 0.1))+x},x);
\end{axis}
\end{tikzpicture}
\end{document}


You can also simplify your code by replacing 2*30 with 60 and so on.

Edit: I don't see this question is a duplicate of Tikz picture of two mathematical functions, asked by the same user 4 hours ago.