a: \(=\dfrac{\left(x-\sqrt{5}\right)\left(x+\sqrt{5}\right)}{x+\sqrt{5}}=x-\sqrt{5}\)
b: \(=\dfrac{-\left(\sqrt{7}-x\right)\left(\sqrt{7}+x\right)}{\sqrt{7}-x}=-x-\sqrt{7}\)
c: \(=\dfrac{\left(x+\sqrt{2}\right)^2}{\left(x+\sqrt{2}\right)\left(x-\sqrt{2}\right)}=\dfrac{x+\sqrt{2}}{x-\sqrt{2}}\)
\(\dfrac{x^2-5}{x+\sqrt{5}}=\dfrac{\left(x+\sqrt{5}\right)\left(x-\sqrt{5}\right)}{x+\sqrt{5}}=x-\sqrt{5}\)
\(\dfrac{x^2-7}{\sqrt{7}-x}=\dfrac{\left(x-\sqrt{7}\right)\left(x+\sqrt{7}\right)}{-\left(x-\sqrt{7}\right)}=-\left(x+\sqrt{7}\right)=-x-\sqrt{7}\)
`( x^2 + 2sqrt{2} +2)/(x^2-2)`
`=(x+sqrt{2})^2/[(x-sqrt{2})(x+sqrt{2})]`
`=(x+sqrt{2})/(x-sqrt{2})`