Question

como resolver esta equação 3/x-1 + 4/x+1 = 4?

Answer 1

$\mathrm{\dfrac{3}{x-1}+\dfrac{4}{x+1}=4\ \to\ MMC=(x-1)(x+1)}\\\\ \mathrm{\dfrac{3(x+1)+4(x-1)}{(x-1)(x+1)}=4\\ \to\ \dfrac{3x+3+4x-4}{x^2-1}=4}\\\\ \mathrm{7x-1=4(x^2-1)\ \to\ 7x-1=4x^2-4}\\ \mathrm{0=4x^2-4-7x+1\ \to\ 0=4x^2-7x-3}\\\\ \textrm{Utilizando a f\'ormula quadr\'atica, obteremos:}\\\\ \mathrm{x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-7)\pm\sqrt{(-7)^2-4.4.(-3)}}{2.4}}\\\\ \mathrm{x=\dfrac{7\pm\sqrt{49+48}}{8}=\dfrac{7\pm\sqrt{97}}{8}}$

$\textrm{Portanto:}\\\\ \mathbf{x=\bigg\{\dfrac{7+\sqrt{97}}{8},\dfrac{7-\sqrt{97}}{8}\bigg\}}$