Question

como chego no resultado x=10/3 da seguinte equação?




4/x-2-x/2x-4 = 7/3x-6

obrigado!

Answer 1

$\dfrac{4}{x-2}-\dfrac{x}{2x-4}=\dfrac{7}{3x-6}\\\\ mmc: (6x+12)\\\\ \dfrac{4(6x-6)-x(3x-3)=7(2x-2)}{6x+12}\\\\ 4(6x-6)-x(3x-3)=7(2x-2)\\\\ 24x-24-3x^2+3x=14x-14\\\\ -3x^2+24x+3x-14x=-14+24\\\\ -3x^2+13x=10\\\\ -3x^2+13x-10=0 (-1)\\\\ 3x^2-13x+10=0$

Aplicando Bháskara:
$x = \dfrac{13\pm\sqrt{169-120}}{6}\\\\ x = \dfrac{13\pm\sqrt{49}}{6}\\\\ x' = \dfrac{13-7}{6}\\ x' = \dfrac{6}{6}\\ \boxed{x' = 1}\\\\ x'' = \dfrac{13+7}{6}\\ x'' = \dfrac{20}{6}\\ \boxed{x'' = \dfrac{10}{3}}$

Bons estudos!