Question

Упростите выражение:

Answer 1

Ответ:

1

Объяснение:

$\frac{\sqrt{a}}{a^{\frac{1}{2}}+b^{\frac{1}{2}}}}- \frac{\sqrt{b}}{a^{\frac{1}{2}}-b^{\frac{1}{2}}}}+\frac{2\sqrt{ab}}{a-b}=\\\\=\frac{\sqrt{a}}{\sqrt{a}+\sqrt{b}}-\frac{\sqrt{b}}{\sqrt{a}-\sqrt{b}}+\frac{2\sqrt{ab}}{a-b}=\\\\=\frac{\sqrt{a}(\sqrt{a}-\sqrt{b})-\sqrt{b}(\sqrt{a}+\sqrt{b})+2\sqrt{ab}}{a-b}=\\\\=\frac{a-\sqrt{ab}-\sqrt{ab}-b+2\sqrt{ab}}{a-b}=\\\\=\frac{a-b}{a-b}=1$

Справочно:

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

$\sqrt{a}*\sqrt{a}=(\sqrt{a})^2=a$