Предмет: Алгебра, автор: snovakeksik

дробь числитель (х+1) * х в квадрате знаменатель 5х - х в квадрате больше или равно 0

Ответы

Автор ответа: Underappreciated

$frac{(x+1)x^2}{5x-x^2}geq0$

$frac{(x+1)x^2}{x(5-x)}geq0$

Правая часть не существует, когда знаменатель равен нулю:

x(5-x) = 0

x = 0; x = 5.

Правая часть равна нулю, когда числитель равен нулю

(x+1)x^2 = 0

x = 0; x = -1

Отмечаем "нули" на числовой прямой и определяем знак:

+ - + -

-------'------0----------0---------->
-1 0 5

х принадлежит $(-infty;-1]cup(0;5)$

Автор ответа: triolana

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