Rational

$\frac{5n}{n-4}+3=\frac{3n+8}{n-4}$

$\frac{2n-12}{n-4}=\frac{3n+8}{n-4}$

$(2n-12)(n-4)=(3n+8)(n-4)$

notice that I don't divide both sides by n-4. (because n-4 can equal 0)

$2n^2-20n+48=3n^2-4n-32$

$n^2+16n-80=0$

$(n+20)(n-4)=0$

$n=-20, n=4$

JP

$N=25- \sqrt(561)/4$

$N=(25+ \sqrt(561))/4$