[attach]26873[/attach]

Matematica

7·(x + 2)/(x + 3) + 5·x/(3 - 2·x) + 2·(x^2 + x - 17)/(9 - 2·x^2 - 3·x) ≤ 0

7·(x + 2)/(x + 3) + 5·x/(3 - 2·x) + 2·(x^2 + x - 17)/((x + 3)·(3 - 2·x)) ≤ 0

(7·((x + 2)·(3 - 2·x)) + 5·x·(x + 3) + 2·(x^2 + x - 17))/((x + 3)·(3 - 2·x)) ≤ 0

(7·(- 2·x^2 - x + 6) + (5·x^2 + 15·x) + (2·x^2 + 2·x - 34))/((x + 3)·(3 - 2·x)) ≤ 0

((- 14·x^2 - 7·x + 42) + (5·x^2 + 15·x) + (2·x^2 + 2·x - 34))/((x + 3)·(3 - 2·x)) ≤ 0

(- 7·x^2 + 10·x + 8)/((x + 3)·(3 - 2·x)) ≤ 0

(7·x^2 - 10·x - 8)/((x + 3)·(3 - 2·x)) ≥ 0

(x - 2)·(7·x + 4)/((x + 3)·(3 - 2·x)) ≥ 0

Segno N(x):

(x - 2)·(7·x + 4) ≥ 0-----> x ≤ - 4/7 ∨ x ≥ 2

Segno D(x):

(x + 3)·(3 - 2·x) > 0---> -3 < x < 3/2

Quindi tabella e soluzione: