Question

Como resolver: 3/x+2+2/x=3x/2x+4

Answer 1

Vamos lá :

$\frac{3}{x+2}+\frac{2}{x}=\frac{3x}{2x+4}$

Mmc 

x+2 , x , 2x + 4 | 2
x +2, x , x + 2 | x + 2
1   , x , 1 | x
1 , 1, 1      ==> 2*(x+2)*x = 2x² + 4x

$\frac{3}{x+2}+\frac{2}{x}=\frac{3x}{2x+4} \\ \\ \frac{3 * 2x}{2x^2 + 4x} + \frac{2*(2x+4)}{2x^2 + 4x} = \frac{3x*x}{2x^2 + 4x} \\ \\ 6x + 4x+8 = 3x^2$
$3x^2-10x - 8 = 0 \\ \\ a = 3 ~~;b = -10~~; c = -8 \\ \\ \Delta = b^2 - 4ac \\ \Delta = (-10)^2 - 4.3.(-8 ) \\ \Delta = 100 + 96 \\ \Delta = 196~~~--\ \textgreater \ \sqrt{\Delta } = 14 \\ \\ \\ x = \frac{-b~ \pm~\sqrt{\Delta }}{2.a} \\ \\ x = \frac{-(-10)~\pm~14}{2.3} \\ \\ x = \frac{10~\pm~14}{6} \\ \\ x' = \frac{10 + 14}{6} = \frac{24}{6} = 4 \\ \\ x'' = \frac{10 - 14}{6} = \frac{- 4~:~2 }{6 ~:~2} = - \frac{2}{3} \\ \\ \\ S = \{- \frac{2}{3} ~,~4\}$

Espero ter ajudado !!!