Question

Scrieți fracțiile rezultate în urma simplificării (x>0):

a)

$\frac{ \sqrt{6} }{2 \sqrt{3} }^{( \sqrt{3} }$

b)

$\frac{ {x}^{3} }{x(x + 1)}^{(x}$

c)

$\frac{x + 2}{ {x}^{2} + 2x }^{(x + 2}$

Answer 1

$\it a)\ \dfrac{\sqrt6^{(\sqrt3}}{2\sqrt3} = \dfrac{\sqrt2}{2} \\ \\ \\ b)\ \dfrac{x^3^{(x}}{x(x+1)}=\dfrac{x^2}{x+1} \\ \\ \\ c)\ \dfrac{x+2}{x^2+2x} = \dfrac{x+2^{(x+2}}{x(x+2)} = \dfrac{1}{x}$

Answer 2

$\dfrac{\sqrt 6}{2\sqrt 3}= \dfrac{\sqrt{3\cdot 2}}{2\sqrt 3}={\dfrac{\sqrt 3\cdot \sqrt 2}{2\sqrt 3}}^{~~(\sqrt 3} = \dfrac{\sqrt 2}{2} \\ \\ \\ \dfrac{x^3}{x(x+1)} =\dfrac{x\cdot x^2}{x(x+1)} ={\dfrac{x^2}{x+1}}^{(x}\\ \\ \\ {\dfrac{x+2}{x^2+2x}} = {\dfrac{x+2}{x(x+2)}}^{(x+2} = \dfrac{1}{x}$