What is -2/x >-(5x)/(x^2+6) ?

The solution to -2/x >-(5x)/(x^2+6) is -2 2

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-2/x >-(5x)/(x^2+6)

- \frac{2}{x} > - \frac{5 x}{x ^{2} + 6}

- 2 < x < 0 or x > 2

Interval Notation

(- 2, 0) \cup (2, \infty)

Solution steps

- \frac{2}{x} > - \frac{5 x}{x ^{2} + 6}

Rewrite in standard form

\frac{3 x ^{2} - 12}{x ( x ^{2} + 6 )} > 0

Factor

\frac{3 x ^{2} - 12}{x ( x ^{2} + 6 )} : \frac{3 ( x + 2 ) ( x - 2 )}{x ( x ^{2} + 6 )}

\frac{3 ( x + 2 ) ( x - 2 )}{x ( x ^{2} + 6 )} > 0

Divide both sides by

3

\frac{\frac{3 ( x + 2 ) ( x - 2 )}{x ( x ^{2} + 6 )}}{3} > \frac{0}{3}

Simplify

\frac{( x + 2 ) ( x - 2 )}{x ( x ^{2} + 6 )} > 0

Identify the intervals

- 2 < x < 0 or x > 2

3 x^{2} - 100 = 500

r^{3} - 25 r^{2} - 9 r + 225

\frac{3 x}{2} + x - 2 = \frac{1}{4} + 2 x

\frac{n + 3}{3 n ^{2} - 10 n + 8} + 3

\frac{1}{2} (10 x - 2) + 3 x = - 25

What is -2/x >-(5x)/(x^2+6) ?
The solution to -2/x >-(5x)/(x^2+6) is -2<x<0\lor x>2