task is x-4 / x^2 + 3x >= 0 solve inequality
x-4 >= 0
x >= 4
x (x+3) , x=0 & x>= -3
thus, (-3,0] and (4, infinity)
is this correct?
By looking at your working I see you mean to solve . You should use brackets to be more clear in future please...
It should be
0 is not included in the first interval as that would cause division by zero. 4 is included in the second interval as we are solving for greater than or equal to 0.
EDIT: sorry fixed a mistake.
Is this correct? . . . . no
You have: . which means: . . . . and that's all.
That fraction is positive if both the numerator and denominator are negtive.
Numerator is negative: .
Denominator is negative: .
There are two cases to consider:
We have: . which means: .
The answer is: .