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enda en ulikhet

Posted: 05/04-2006 18:09
by ----
(4x-3)/(x i annen - 2x-3) > 2/(x+1)

Posted: 05/04-2006 19:32
by Solar Plexsus
(4x - 3) / (x[sup]2[/sup] - 2x - 3) > 2/(x + 1)

(4x - 3) / [(x - 3)(x + 1)] - 2/(x + 1) > 0

[(4x - 3) - 2(x - 3)] / [(x - 3)(x + 1)] > 0

(4x - 3 - 2x + 6) / [(x - 3)(x + 1)] > 0

(2x + 3) / [(x - 3)(x + 1)] > 0

Vha. av et fortegnsskjema for (2x - 3) / [(x - 3)(x + 1)] finner vi at løsningen av denne ulikheten blir xε(-3/2,-1)U(3,->).