Question

Упростите выражение. Подробно пожалуйста.

Answer 1

$\Big(\dfrac{1}{\sqrt{a}-\sqrt{a-b}}+\dfrac{1}{\sqrt{a}+\sqrt{a+b}}\Big):\Big(1+\sqrt{\dfrac{a+b}{a-b}}\Big)=\\\\\\=\left (\dfrac{\sqrt{a}+\sqrt{a-b}}{(\sqrt{a}-\sqrt{a-b})(\sqrt{a}+\sqrt{a-b})}}+\dfrac{\sqrt{a}-\sqrt{a+b}}{(\sqrt{a}+\sqrt{a+b})(\sqrt{a}-\sqrt{a+b})}\right ):\Big(1+\dfrac{\sqrt{a+b}}{\sqrt{a-b}}\Big)=\\\\\\=\left(\dfrac{\sqrt{a}+\sqrt{a-b}}{a-(a-b)}+\dfrac{\sqrt{a}-\sqrt{a+b}}{a-(a+b)}\right)\cdot \dfrac{\sqrt{a-b}}{\sqrt{a-b}+\sqrt{a+b}}=$

$=\dfrac{\sqrt{a}+\sqrt{a-b}}{b}+\dfrac{\sqrt{a}-\sqrt{a+b}}{-b}\cdot \dfrac{\sqrt{a-b}}{\sqrt{a-b}+\sqrt{a+b}}=\\\\\\=\dfrac{\sqrt{a}+\sqrt{a-b}-\sqrt{a}+\sqrt{a+b}}{b}\cdot \dfrac{\sqrt{a-b}}{\sqrt{a-b}+\sqrt{a+b}}=\\\\\\=\dfrac{\sqrt{a-b}+\sqrt{a+b}}{b}\cdot \dfrac{\sqrt{a-b}}{\sqrt{a-b}+\sqrt{a+b}}=\dfrac{\sqrt{a-b}}{b}$