Question

освободитесь от иррациональности в знаменателе дроби: a/√3; 3/√11-√2

Answer 1

$frac{a}{sqrt{3}}=frac{asqrt{3}}{sqrt{3}*sqrt{3}}=frac{asqrt{3}}{3}$
-----------------
$frac{3}{sqrt{11}-sqrt{2}}=frac{3*(sqrt{11}+sqrt{2})}{(sqrt{11}-sqrt{2})*(sqrt{11}+sqrt{2})}$
$=frac{3*(sqrt{11}+sqrt{2})}{(sqrt{11})^2-(sqrt{2})^2}$
$=frac{3*(sqrt{11}+sqrt{2})}{11-2}$
$=frac{3*(sqrt{11}+sqrt{2})}{9}=$
$frac{sqrt{11}+sqrt{2}}{3}$