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

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

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

\frac{( 2 x ^{2} )}{( x - 5 )} > - 5

- 5 < x < \frac{5}{2} or x > 5

Interval Notation

(- 5, \frac{5}{2}) \cup (5, \infty)

Decimal Notation

- 5 < x < 2.5 or x > 5

Solution steps

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

Rewrite in standard form

\frac{2 x ^{2} + 5 ( x - 5 )}{x - 5} > 0

Factor

\frac{2 x ^{2} + 5 ( x - 5 )}{x - 5} : \frac{( x + 5 ) ( 2 x - 5 )}{x - 5}

\frac{( x + 5 ) ( 2 x - 5 )}{x - 5} > 0

Identify the intervals

- 5 < x < \frac{5}{2} or x > 5

\frac{3}{( x - 2 ) - 1} < 0

6 x^{3} - x^{2} < 8 - 48 x

(x + 5) (x + 8) > 0

\frac{x}{( x ^{2} + 3 x + 2 )} > \frac{1}{( x + 1 )}

2 x^{2} > 3 x

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