Question

halla el c.s de x+1/x-1-1=x+4/x-2​

Answer 1

Explicación paso a paso:

$\dfrac{x+1}{x-1} - 1 = \dfrac{x+4}{x-2} \\ \\ \\ \dfrac{x+1-(x - 1)}{x-1} = \dfrac{x+4}{x-2} \\ \\ \\ \dfrac{\not{x}+1\not{-x}+1}{x-1} = \dfrac{x+4}{x-2} \\ \\ \\ \dfrac{2}{x-1} = \dfrac{x+4}{x+2} \\ \\ \\ 2(x + 2) = (x + 4)(x - 1) \\ \\ 2x + 4 = x^{2} + 3x - 4 \\ \\ x^{2} + x - 8 = 0$

$\textbf{Aplicando Formula General.} \\ \\ \boxed{x_{1,2} = \dfrac{-b\ñ\sqrt{b^{2} -4ac } }{2a}} \\ \\ \\ Donde : \\ \\ a = 1\ \ \  ;\ \ \ b = 1 ;\ \ \  c = - 8$

$x_{1,2} = \dfrac{-1\ñ\sqrt{1 - 4(1)(8)} }{2(1)} \\ \\ \\ x_{1,2} = \dfrac{-1\ñ\sqrt{-31}}{2}  \\ \\ \\ \boxed{x_{1} = \frac{-1 + \sqrt{31i}}{2}}  \\ \\ \\ \boxed{x_{2} = \frac{- 1 - \sqrt{31i}}{2}}$

Nota :

Cuando al discriminante (Δ) < 0 las raíces son cantidad imaginarias y conjugadas.