г) $\dfrac{1}{\sqrt{3}-\sqrt{2}}-\dfrac{1}{\sqrt{3}+\sqrt{2}}$;

Question

Вопрос: $Фото задания: г) $\dfrac{1}{\sqrt{3}-\sqrt{2}}-\dfrac{1}{\sqrt{3}+\sqrt{2}}$;$ Фото задания

Accepted Answer

Рационализируем знаменатели:

\[\frac{1}{\sqrt{3}-\sqrt{2}}=\frac{\sqrt{3}+\sqrt{2}}{3-2}=\sqrt{3}+\sqrt{2},\]

\[\frac{1}{\sqrt{3}+\sqrt{2}}=\frac{\sqrt{3}-\sqrt{2}}{3-2}=\sqrt{3}-\sqrt{2}.\]

Тогда:

\[(\sqrt{3}+\sqrt{2})-(\sqrt{3}-\sqrt{2})=2\sqrt{2}.\]

Ответ: $2\sqrt{2}$.

г) \(\dfrac{1}{\sqrt{3}-\sqrt{2}}-\dfrac{1}{\sqrt{3}+\sqrt{2}}\);