Question

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

Answer 1

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