What is (6x^3-13x^2-5x)/(x^2-4)>= 0 ?

The solution to (6x^3-13x^2-5x)/(x^2-4)>= 0 is -2 = 5/2

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(6x^3-13x^2-5x)/(x^2-4)>= 0

\frac{6 x ^{3} - 13 x ^{2} - 5 x}{x ^{2} - 4} \geq 0

- 2 < x \leq - \frac{1}{3} or 0 \leq x < 2 or x \geq \frac{5}{2}

Interval Notation

(- 2, - \frac{1}{3}] \cup [0, 2) \cup [\frac{5}{2}, \infty)

Decimal Notation

- 2 < x \leq - 0.33333 \dots or 0 \leq x < 2 or x \geq 2.5

Solution steps

\frac{6 x ^{3} - 13 x ^{2} - 5 x}{x ^{2} - 4} \geq 0

Factor

\frac{6 x ^{3} - 13 x ^{2} - 5 x}{x ^{2} - 4} : \frac{x ( 3 x + 1 ) ( 2 x - 5 )}{( x + 2 ) ( x - 2 )}

\frac{x ( 3 x + 1 ) ( 2 x - 5 )}{( x + 2 ) ( x - 2 )} \geq 0

Identify the intervals

- 2 < x \leq - \frac{1}{3} or 0 \leq x < 2 or x \geq \frac{5}{2}

\frac{1}{2 \cdot 1 0 ^{9}}

\frac{1}{\frac{1}{8}}

lo g_{e} (3)

(x - 8) (x - 4) (x - 2) > 0

4 x^{2} - 4 x + 6

What is (6x^3-13x^2-5x)/(x^2-4)>= 0 ?
The solution to (6x^3-13x^2-5x)/(x^2-4)>= 0 is -2<x<=-1/3 \lor 0<= x<2\lor x>= 5/2