Remove["Global`*"]
xv={1,2.5,4,6,8};
yv={1,1.5,2,2.5,3};
data=Transpose[Append[{xv},yv]];
y = (x/((a*x+b)));
z=x/y;
zv =xv/yv;
𝔸={#,1}&/@data[[All,1]];
p={a,b};
𝔸T =Transpose[𝔸];
sol = Solve[𝔸T.𝔸.p == 𝔸T.zv,{a,b}];
Print["Min lösning:      ",FullSimplify[sol[[1]]]];
pf = FindFit[data,(x/(a*x+b)),{a,b},x];
Print["Mathematicas Fit: ",pf]
answer = y/.sol;
pl=Plot[answer,{x,xv[[1]],xv[[5]]},PlotLegends->{"Min"}];
pfp = Plot[y/.pf,{x,xv[[1]],xv[[5]]} ,PlotStyle->{Green,Dashed}, PlotLegends->{"Fit"}];
lp=ListPlot[data,PlotStyle->{Red,PointSize[Large]}];
Show[{lp,pl, pfp}]