(х^2 *(х - 3))/ (х - 1) < 0

Предыдущий
вопрос Следующий
вопрос

To solve this inequality, we first need to find the critical points by setting the numerator and the denominator equal to 0:

Numerator:
x^2 = 0 or x - 3 = 0
x = 0 or x = 3

Denominator:
x - 1 = 0
x = 1

Now, we can create a number line with these critical points at 0, 1, and 3. We will test each interval to determine where the function is less than 0:

For x < 0:
(-) * (-) / (-) = positive / negative = negative

For 0 < x < 1:
(+) * (-) / (-) = positive / positive = negative

For 1 < x < 3:
(+) * (+) / (+) = positive / positive = positive

For x > 3:
(+) * (+) / (+) = positive / positive = positive

Therefore, the solution to the inequality is x < 0 or 0 < x < 1.