What is ((9-X^2))/(X(X-1)^2)<= 0 ?

The solution to ((9-X^2))/(X(X-1)^2) = 3

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((9-X^2))/(X(X-1)^2)<= 0

\frac{( 9 - X ^{2} )}{X ( X - 1 ) ^{2}} \leq 0

- 3 \leq X < 0 or X \geq 3

Solution steps

\frac{9 - X ^{2}}{X ( X - 1 ) ^{2}} \leq 0

Factor

\frac{9 - X ^{2}}{X ( X - 1 ) ^{2}} : \frac{- ( X + 3 ) ( X - 3 )}{X ( X - 1 ) ^{2}}

\frac{- ( X + 3 ) ( X - 3 )}{X ( X - 1 ) ^{2}} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( X + 3 ) ( X - 3 ) ) ( - 1 )}{X ( X - 1 ) ^{2}} \geq 0 \cdot (- 1)

Simplify

\frac{( X + 3 ) ( X - 3 )}{X ( X - 1 ) ^{2}} \geq 0

Identify the intervals

- 3 \leq X < 0 or X \geq 3

\frac{5 ( 2 ) ^{\frac{1}{3}}}{3}

2. 7^{2}

∣ 4 x + 8 ∣ > - 4

x^{4} + x^{2}

(3 x + 2) (x + 1) = 0

What is ((9-X^2))/(X(X-1)^2)<= 0 ?
The solution to ((9-X^2))/(X(X-1)^2)<= 0 is -3<= X<0\lor X>= 3