What is (12x(x^3-2))/((x^3+1)^3)<= 0 ?

The solution to (12x(x^3-2))/((x^3+1)^3)<= 0 is x<-1\lor 0<= x<= \sqrt[3]{2}

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(12x(x^3-2))/((x^3+1)^3)<= 0

\frac{12 x ( x ^{3} - 2 )}{( x ^{3} + 1 ) ^{3}} \leq 0

Interval Notation

Decimal Notation

x < - 1 or 0 \leq x \leq 1.25992 \dots

Solution steps

\frac{12 x ( x ^{3} - 2 )}{( x ^{3} + 1 ) ^{3}} \leq 0

Rewrite in standard form

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

Factor

Identify the intervals

f = 4 (3.9822) - (3.9822)^{2}

3 x^{2} - 42 = 0

x^{2} - 16 + 64

- 3 - 2 x > 9

w + 16 < 4

What is (12x(x^3-2))/((x^3+1)^3)<= 0 ?
The solution to (12x(x^3-2))/((x^3+1)^3)<= 0 is x<-1\lor 0<= x<= \sqrt[3]{2}