Question

2/ x-3 + 5/ x+3 = 3 / 2( x - 1)

Answer 1

Respuesta:

$x=\frac{3+\sqrt{177}}{6},\:x=\frac{3-\sqrt{177}}{6}$

Explicación paso a paso:

$\frac{2}{x}-3+\frac{5}{x}+3=\frac{3}{2}\left(x-1\right)\\\\\mathrm{Multiplicamos\:por\:el\:minimo\:comun\:multiplo=}2x\\\\\frac{2}{x}\cdot \:2x-3\cdot \:2x+\frac{5}{x}\cdot \:2x+3\cdot \:2x=\frac{3}{2}\left(x-1\right)\cdot \:2x\\\\simplificamos\\\\14=3x\left(x-1\right)\\\\\mathrm{Resolvemos\:}\:14=3x\left(x-1\right):\quad x=\frac{3+\sqrt{177}}{6},\:x=\frac{3-\sqrt{177}}{6}\\\\x=\frac{3+\sqrt{177}}{6},\:x=\frac{3-\sqrt{177}}{6}$