Question

Resolver a inequação em R (reais )

2/3x-1 >= 1/X-1 - 1/X+1

Answer 1

Explicação passo-a-passo:

Inequação:

$\mathsf{\dfrac{2}{3x-1}~≥~\dfrac{1}{x-1}-\dfrac{1}{x+1} }$

$\mathsf{\dfrac{2}{3x-1}~≥~\dfrac{x+1-(x-1)}{(x-1)(x+1)} }$

$\mathsf{\dfrac{2}{3x-1}~≥~\dfrac{x+1-x+1 }{x^2+x-x-1} }$

$\mathsf{\dfrac{\cancel{2}}{3x-1}~≥~\dfrac{\cancel{2}}{x^2-1} }$

$\mathsf{3x\cancel{-1}~≥~x^2\cancel{-1} }$

$\mathsf{x^2~≤~3x }$

$\mathsf{x^2-3x~≤~0 }$

$\mathsf{x\Big(x-3\Big)~≤~0 }$

$\mathsf{x~≤~0~V~x-3~≤~0 }$

$\mathsf{x~≤~0~V~x~≤~3 }$

Sol: x€ ] -∞ ; 0 ] U ] -∞ ; 3 ]

Sol: x€ [ 0 ; 3 ]

Espero ter ajudado bastante!)