What is (x-x^3)/(x+3)>= 0 ?

The solution to (x-x^3)/(x+3)>= 0 is -3<x<=-1\lor 0<= x<= 1

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(x-x^3)/(x+3)>= 0

\frac{x - x ^{3}}{x + 3} \geq 0

- 3 < x \leq - 1 or 0 \leq x \leq 1

Interval Notation

(- 3, - 1] \cup [0, 1]

Solution steps

\frac{x - x ^{3}}{x + 3} \geq 0

Factor

\frac{x - x ^{3}}{x + 3} : \frac{- x ( x + 1 ) ( x - 1 )}{x + 3}

\frac{- x ( x + 1 ) ( x - 1 )}{x + 3} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - x ( x + 1 ) ( x - 1 ) ) ( - 1 )}{x + 3} \leq 0 \cdot (- 1)

Simplify

\frac{x ( x + 1 ) ( x - 1 )}{x + 3} \leq 0

Identify the intervals

- 3 < x \leq - 1 or 0 \leq x \leq 1

x + 2 < 3 x - 2

1.4 5^{- 0.7}

\frac{9 x + 5}{8} = 4

- 9 - 35

5 x - 3 < 7 x + 7

What is (x-x^3)/(x+3)>= 0 ?
The solution to (x-x^3)/(x+3)>= 0 is -3<x<=-1\lor 0<= x<= 1