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# Solve the inequality (x^2(9+x)(x-6))/((x+5)(x-2))> or equal to 0

This is a fraction     x^2(9+x)(x-6) is the numerator  (x+5)(x-2) is the denominator and it's all set to greater than or equal to 0

### 4 Answers by Expert Tutors

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
1

Solve (x^2(9+x)(x-6))/((x+5)(x-2)) = 0,

x = -9, 0, 6

Solve (x^2(9+x)(x-6))/((x+5)(x-2)) > 0 by checking the intervals (-oo, -9), (-9, -5), (-5, 0), (0, 2), (2, 6) and (6, oo).

x = (-9, -5) U (0, 2) U (6, oo)

Combining the solution for inequality with the solution for equality gives you the final answer.

Answer: [-9, -5) U [0, 2) U [6, oo)

Hi Robert. If I "plug in" (-8), the given inequality will be negative .... but (-4) satisfy given inequality ....

Katherine P. | Shoreview Area Math Tutoring and Test PrepShoreview Area Math Tutoring and Test Pr...
5.0 5.0 (569 lesson ratings) (569)
1

I think you would want to solve this with a graph, because you will be getting ranges for values of x.

1. Search for "graphing calculator"

2. Type your  equation into the graphing calculator's y = ________ box.

For the link above, you need to add asterisk marks for multiplication:

(x^2*(9+x)*(x-6))/((x+5)*(x-2))

3. Take a look at the graph. Note the values of x where y is greater than or equal to 0, those are the ranges of x that fit your inequality.

x<___ , ___ < x < ___ , x > ___

If this helps, please vote for the answer. Let me know if you need more help! :)

Brian B. | Making Math Matter...and Easy to Understand! Making Math Matter...and Easy to Underst...
5.0 5.0 (226 lesson ratings) (226)
1

Multiply both sides by the denominator, which will leave us with the numerator >= to zero, than look at the critical point that make the numerator go to zero, namely 0, -9 , and 6.  Next test points to the right and left of these values to see if it makes the inequality true...remember x cannot equal -5, or +2 because of the denominator. Start testing regions between these critical points to locate the solution regions.

Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
0

<-------•---•---•---o---•-----•---•----o----•---•---•------->
-∞    -10  -9  -8   -5  -4      0   1    2     4    6   7       +∞
-9 , -5 , 0, 2, 6 - are critical points; (-10, -8, -4, 1, 4, 7 - just control points) so the answer is:
(-∞,-9] U (-5,2) U (2, +∞)