观察下列运算过程：

$\begin{array}{c}\frac{1}{1+\sqrt{2}}=\frac{1}{\sqrt{2}+1}=\frac{\sqrt{2}-1}{(\sqrt{2}+1)(\sqrt{2}-1)}=\frac{\sqrt{2}-1}{{\left(\sqrt{2}\right)}^2-1^2}=\sqrt{2}-1\\ \frac{1}{\sqrt{2}+\sqrt{3}}=\frac{1}{\sqrt{3}+\sqrt{2}}=\frac{\sqrt{3}-\sqrt{2}}{(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})}=\frac{\sqrt{3}-\sqrt{2}}{{\left(\sqrt{3}\right)}^2-{\left(\sqrt{2}\right)}^2}=\sqrt{3}-\sqrt{2}\\ \dots \dots \end{array}$

请运用上面的运算方法计算： $\frac{1}{1+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{7}}+\dots +\frac{1}{\sqrt{2015}+\sqrt{2017}}+\frac{1}{\sqrt{2017}+\sqrt{2019}}=$　　．

科目 数学   题型 填空题   难度 中等

知识点： 二次根式的混合运算