Question

$6x + 5 = \frac{3x + 5}{x - 1}$
(com x E R e x diferente de 1)​

Answer 1

$6x + 5 = \frac{3x + 5}{x - 1}$

Multiplicando tudo por x-1

$(6x + 5) \times (x - 1) = 3x + 5$

$(6x + 5) \times (x - 1) - 3x - 5 = 0$

$6 {x}^{2} - 6x + 5x - 5 - 3x - 5 = 0$

${6x}^{2} - 4x - 10 = 0$

$3 {x}^{2} - 2x - 5 = 0$

∆ = (-2)² - 4.3.(-5)

∆ = 4 + 60

∆ = 64

$x = \frac{ - ( - 2) + - \sqrt{64} }{2 \times 3}$

$x = \frac{2 + - 8}{6}$

$x = \frac{2 + 8}{6} = \frac{5}{3} \\ x = \frac{2 - 8}{6} = - 1$