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

The solution to ((x-2)^2*(x^2-3))/(((x+1)^3))<0 is x<-sqrt(3)\lor-1<x<sqrt(3)

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

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

x < - 3 or - 1 < x < 3

Interval Notation

(- \infty, - 3) \cup (- 1, 3)

Decimal Notation

x < - 1.73205 \dots or - 1 < x < 1.73205 \dots

Solution steps

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

Factor

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

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

Identify the intervals

x < - 3 or - 1 < x < 3

\frac{( x + 4 )}{( x - 2 )} < \frac{2}{( x + 1 )}

(x - 2)^{3} > 0

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

(x - 1) (x + 2) - (x + 2) (x - 3) > 0

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

What is ((x-2)^2*(x^2-3))/(((x+1)^3))<0 ?
The solution to ((x-2)^2*(x^2-3))/(((x+1)^3))<0 is x<-sqrt(3)\lor-1<x<sqrt(3)