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

\frac{( 6 )}{( x ^{2} - 4 x + 4 )} > 0

\frac{1}{2 ( 4 x + 14 )} < 3 x - 6

\frac{( 3 p + 5 )}{( 5 p - 9 )} > \frac{2}{7}

(a - 2) (3 a) < 0

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