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

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

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

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

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

Interval Notation

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

Solution steps

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

Factor

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

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

Identify the intervals

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

(x - 1)^{2} < 25

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

(x - 4)^{2} > 0

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

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

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