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

The solution to (((x-1)*(x+2)^2))/((-1-x)) 1

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

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

x < - 2 or - 2 < x < - 1 or x > 1

Interval Notation

(- \infty, - 2) \cup (- 2, - 1) \cup (1, \infty)

Solution steps

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

Identify the intervals

x < - 2 or - 2 < x < - 1 or x > 1

\frac{1}{x ^{3}} > - 27

\frac{( 2 x - 4 )}{( 3 - x )} \geq 1

\frac{( ( x + 2 ) ( x ^{2} - 2 x + 1 ) )}{( 4 + 3 x - x ^{2} )} \geq 0

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

\frac{( 5 - 2 x )}{( 3 x ^{2} - 2 x - 16 )} < 1

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