Математика, 11 класс

Решите задачу:

$( \frac{ \sqrt{m}-2 }{ \sqrt{m}+2 }+ \frac{8 \sqrt{m} }{(\sqrt{m}+2)(\sqrt{m}-2)} )* \frac{\sqrt{m}(\sqrt{m}-2)}{\sqrt{m}+2} =\\ =( \frac{ (\sqrt{m}-2)^2 }{( \sqrt{m}+2)(\sqrt{m}-2) }+ \frac{8 \sqrt{m} }{(\sqrt{m}+2)(\sqrt{m}-2)} )* \frac{\sqrt{m}(\sqrt{m}-2)}{\sqrt{m}+2} =\\ = \frac{m-4 \sqrt{m}+4+8 \sqrt{m} }{(\sqrt{m}+2)(\sqrt{m}-2)} * \frac{\sqrt{m}(\sqrt{m}-2)}{\sqrt{m}+2} =$ $= \frac{m+4 \sqrt{m}+4 }{\sqrt{m}+2} * \frac{\sqrt{m}}{\sqrt{m}+2} = \frac{\sqrt{m}(\sqrt{m}+2)^2}{(\sqrt{m}+2)^2} =\\ =\sqrt{m}$