What is x->(-2(8+x^3))/((x^2-4)) ?

The solution to x->(-2(8+x^3))/((x^2-4)) is x>2

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x->(-2(8+x^3))/((x^2-4))

x - > \frac{- 2 ( 8 + x ^{3} )}{( x ^{2} - 4 )}

x > 2

Interval Notation

(2, \infty)

Solution steps

x > \frac{- 2 ( 8 + x ^{3} )}{x ^{2} - 4}

Rewrite in standard form

\frac{3 x ^{3} - 4 x + 16}{x ^{2} - 4} > 0

Factor

\frac{3 x ^{3} - 4 x + 16}{x ^{2} - 4} : \frac{( x + 2 ) ( 3 x ^{2} - 6 x + 8 )}{( x + 2 ) ( x - 2 )}

\frac{( x + 2 ) ( 3 x ^{2} - 6 x + 8 )}{( x + 2 ) ( x - 2 )} > 0

Identify the intervals

x > 2

(x + 2) \cdot (x - 3) > (2 - x) \cdot (6 - x)

(\frac{( - 18 x ^{2} + 18 )}{( x ^{2} + 3 ) ^{3}}) > 0

\frac{( ( x ^{2} + x + 1 ) ( x + 2 ) )}{( x ^{2} + 4 x + 5 )} > 0

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

\frac{( x ^{2} + 6 x - 11 )}{( x + 3 )} < - 1

What is x->(-2(8+x^3))/((x^2-4)) ?
The solution to x->(-2(8+x^3))/((x^2-4)) is x>2