Question

Укажите множество решений неравенства. x+2/(x-2)(3-x) меньше или равно 0 помогите пожалуйста!!!!

Answer 1

ОДЗ:

x-2 не равен 0     х не равен 2

3-х не равен 0     х не равен 3

D(f)=R\{2,3}

 x+2=0     x=-2

 x-2=0      x=2

 3-x=0      x=3

 

S=[-2;2) в объединении (-3;+бесконечность)

Answer 2

Solution to the Inequality

To find the solution to the inequality x + 2/(x-2)(3-x) <= 0, we can start by finding the critical points and then determining the intervals where the inequality holds true.

Critical Points

The critical points are the values of x that make the expression undefined or equal to zero. In this case, the critical points are the values of x that make the denominator zero and the numerator zero.

The critical points are: 1. x = 2 2. x = 3

Intervals

We can use these critical points to create intervals and test the inequality within each interval.

- For x < 2, the expression is undefined. - For 2 < x < 3, the expression is negative. - For x > 3, the expression is positive.

Conclusion

Therefore, the solution to the inequality x + 2/(x-2)(3-x) <= 0 is: - x <= 2 - 2 < x < 3

This means that the inequality is satisfied when x is less than or equal to 2, and when x is between 2 and 3.