Question

$(a-5)/(a+2\sqrt{5}+5)$

Answer 1

$\frac{a-5}{a+2\sqrt{5a}+5 } =\frac{(\sqrt{a})^{2}-(\sqrt{5})^{2}}{(\sqrt{a})^{2}+2\sqrt{5a}+(\sqrt{5})^{2}}=\frac{(\sqrt{a}-\sqrt{5})(\sqrt{a}+\sqrt{5})}{(\sqrt{a}+\sqrt{5})^{2}}=\frac{\sqrt{a}-\sqrt{5}}{\sqrt{a}+\sqrt{5}}$