smc

$\frac{a}{b}+\frac{b}{a}-ab=\frac{a^2+b^2}{ab}-(a-b)=\frac{a^2+b^2}{a-b}-\frac{(a-b{)}^2}{(a-b)}=\frac{2ab}{a-b}=\frac{2(a-b)}{a-b}=2\Rightarrow \boxed{2}$. Another way is to solve the equation for $b,$ giving $b=\frac{a}{a+1};$ then substituting this into the expression and simplifying gives the answer of $2.$