Question

Vaaa rog urgenttt dau test mâine ex 26 COROANAAA 35 pct

Answer 1

$\displaystyle a)E(x)=\left( \frac{3}{x+3}+ \frac{2}{x-3} + \frac{3}{x^2-9} \right):\left(1+ \frac{x^2+9}{x^2-9} \right) \\ \\ E(x)=\left( \frac{3}{x+3}+ \frac{2}{x-3} + \frac{3}{(x-3)(x+3)} \right):\left(1+ \frac{x^2+9}{(x-3)(x+3)} \right)\\ \\ E(x)= \frac{3(x-3)+2(x+3)+3}{(x-3)(x+3)} : \frac{(x-3)(x+3)+x^2+9}{(x-3)(x+3)} \\ \\ E(x)= \frac{3x-9+2x+6+3}{(x-3)(x+3)} \cdot \frac{(x-3)(x+3)}{x^2-9+x^2+9} \\ \\ E(x)=5x \cdot \frac{1}{2x^2} \\ \\ E(x)= \frac{5}{2x}$
$\displaystyle b)x= \frac{1}{ \sqrt{3}-1 } - \frac{1}{ \sqrt{3}+1 } \\ \\ E(x)= \frac{5}{2x} \\ \\ E(x)= \frac{5}{2\left(\frac{1}{ \sqrt{3}-1 } - \frac{1}{ \sqrt{3}+1 }\right)}= \frac{5}{2 \cdot \frac{ \sqrt{3}+1- \sqrt{3}+1 }{2} } = \frac{5}{2}$
$\displaystyle c)2a \cdot E(a)=a+6 \\ \\ 2a \cdot \frac{5}{2a} =a+6\Rightarrow 5=a+6 \Rightarrow -a=6-5 \Rightarrow -a=1 \Rightarrow a=-1$