Question Number 227426 by Elie last updated on 25/Jan/26
$${Un}\:=\:\frac{\mathrm{5}{n}−\mathrm{3}}{\mathrm{3}{n}−\mathrm{5}} \\ $$$${Un}\:=\:\frac{{n}\left(\mathrm{5}−\frac{\mathrm{3}}{{n}}\right)}{{n}\left(\mathrm{3}−\frac{\mathrm{5}}{{n}}\right)} \\ $$$${Un}\:=\:\frac{\left(\mathrm{5}−\frac{\mathrm{3}}{{n}}\right)}{\left(\mathrm{3}−\frac{\mathrm{5}}{{n}}\right)} \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}{Un}\:=\:\frac{\left(\mathrm{5}−\frac{\mathrm{3}}{\infty}\right)}{\left(\mathrm{3}−\frac{\mathrm{5}}{\infty}\right)}=\:\frac{\mathrm{5}}{\mathrm{3}} \\ $$$${Good}\:{Luck} \\ $$