[tex]\displaystyle \\
a)~~~ \frac{x^2-5}{x+ \sqrt{5}} =\frac{(x- \sqrt{5})(x+ \sqrt{5})}{x+ \sqrt{5}}=\boxed{x- \sqrt{5}} \\ \\
b)~~~ \frac{3+ \sqrt{a}}{3\sqrt{a}+a}=\frac{3+ \sqrt{a}}{\sqrt{a}(3+\sqrt{a})}=\boxed{\frac{1}{\sqrt{a}}}=\boxed{\frac{\sqrt{a}}{a}} [/tex]
[tex]\displaystyle \\
c)~~~ \frac{ \sqrt{2}-2 }{\sqrt{2}-1}=\frac{ \sqrt{2}(1-\sqrt{2}) }{\sqrt{2}-1}=-\frac{ \sqrt{2}
(\sqrt{2}-1) }{\sqrt{2}-1}=\boxed{-\sqrt{2}} \\ \\
d)~~~ \frac{2 \sqrt{7}-7 }{\sqrt{7}}= \frac{\sqrt{7}(2-\sqrt{7})}{\sqrt{7}}=\boxed{2-\sqrt{7}}[/tex]
