Question

ayuda rapido porfavor

Answer 1

(6)

$\dfrac{2x}{x+3}\geq 1\\ \\ \\ \dfrac{2x}{x+3}-1\geq 0\\ \\ \\ \dfrac{x-3}{x+3}\geq 0\\ \\ \\ (x-3)(x+3)\geq 0 \wedge x\neq -3\\ \\ x\in (-\infty,-3]\cup[3,+\infty)\wedge x\neq -3\\ \\ \boxed{x\in (-\infty,-3)\cup[3,+\infty)}$

(7)

$\dfrac{x(x+5)}{x-3}\geq 0\\ \\ x(x+5)(x-3)\geq 0\wedge x\neq 3\\ \\ x\in [-5,0]\cup [3,+\infty)\wedge x\neq 3\\ \\ \boxed{x\in [-5,0]\cup (3,+\infty)}$

(8)

$\dfrac{2}{x+1}\geq \dfrac{1}{x-2}\\ \\ \\ \dfrac{2}{x+1}- \dfrac{1}{x-2}\geq0\\ \\ \\ \dfrac{x-5}{(x+1)(x-2)}\geq 0\\ \\ \\ (x-5)(x+1)(x-2)\geq 0\wedge x\neq -1\wedge x\neq 2\\ \\ \\ x\in [-1,2]\cup[5,+\infty)\wedge x\neq -1\wedge x\neq 2\\ \\ \\ \boxed{x\in (-1,2)\cup[5,+\infty)}$