$\frac{1}{t_n-s_n}(-t_ne^{-t_n}-e^{-t_n}+s_ne^{-s_n}+e^{-s_n}) \to 0$, as $t_n-s_n \to +\infty$

Question

I am trying to show that $$\frac{1}{t_n-s_n}(-t_ne^{-t_n}-e^{-t_n}+s_ne^{-s_n}+e^{-s_n}) \to 0$$ $$\frac{1}{t_n-s_n}(t_n-e^{-t_n}-s_n+e^{-s_n}) \to 1$$ as $t_n-s_n \to +\infty$, with $t_n > s_n$, $\forall n.$

Any help would be great.