Question

упростите выражение (√n/√m+√n-√n-√m/√n):√m/√n

Answer 1

Ответ:

$\frac{\sqrt{m}}{\sqrt{m}+\sqrt{n}}$

Пошаговое объяснение:

$(\frac{\sqrt{n}}{\sqrt{m}+\sqrt{n}}-^{^1}\frac{\sqrt{n}-\sqrt{m}}{\sqrt{n}}):^{^2}\frac{\sqrt{m}}{\sqrt{n}}=\frac{\sqrt{m}}{\sqrt{m}+\sqrt{n}}$

1)

$\frac{\sqrt{n}}{\sqrt{m}+\sqrt{n}}-\frac{\sqrt{n}-\sqrt{m}}{\sqrt{n}}=\frac{\sqrt{n}}{\sqrt{m}+\sqrt{n}}+\frac{-(\sqrt{n}-\sqrt{m})}{\sqrt{n}}=\frac{\sqrt{n}}{\sqrt{m}+\sqrt{n}}^{(\sqrt{n}}+\frac{\sqrt{m}-\sqrt{n}}{\sqrt{n}}^{(\sqrt{m}+\sqrt{n}}=\\\\=\frac{(\sqrt{n})^2+(\sqrt{m}-\sqrt{n})(\sqrt{m}+\sqrt{n})}{(\sqrt{m}+\sqrt{n})\cdot\sqrt{n}} =\frac{n+(\sqrt{m})^2-(\sqrt{n})^2}{(\sqrt{m}+\sqrt{n})\cdot\sqrt{n}} =\frac{n+m-n}{(\sqrt{m}+\sqrt{n})\cdot\sqrt{n}} =\frac{m}{(\sqrt{m}+\sqrt{n})\cdot\sqrt{n}}$

2)

$\frac{m}{(\sqrt{m}+\sqrt{n})\cdot\sqrt{n}}:\frac{\sqrt{m}}{\sqrt{n}}=\frac{m}{(\sqrt{m}+\sqrt{n})\cdot\sqrt{n}}\cdot\frac{\sqrt{n}}{\sqrt{m}}=\frac{(\sqrt{m})^2}{(\sqrt{m}+\sqrt{n})\cdot\sqrt{m}}=\frac{\sqrt{m}}{\sqrt{m}+\sqrt{n}}$