What is (((x-1)^2*(x+1)^3))/((x^4*(x-2)))<0 ?

The solution to (((x-1)^2*(x+1)^3))/((x^4*(x-2)))<0 is -1<x<0\lor 0<x<1\lor 1<x<2

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(((x-1)^2(x+1)^3))/((x^4(x-2)))<0

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

- 1 < x < 0 or 0 < x < 1 or 1 < x < 2

Interval Notation

(- 1, 0) \cup (0, 1) \cup (1, 2)

Solution steps

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

Identify the intervals

- 1 < x < 0 or 0 < x < 1 or 1 < x < 2

\frac{3 \cdot ( 1 - x )}{2 + 2 x - 1} > \frac{3 x - 1}{2}

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

x^{2} + 3 x + 1 < 0

121 x^{2} - 22 x + 1 < 0

(x^{2} + 3 x + 13) > 0

What is (((x-1)^2*(x+1)^3))/((x^4*(x-2)))<0 ?
The solution to (((x-1)^2*(x+1)^3))/((x^4*(x-2)))<0 is -1<x<0\lor 0<x<1\lor 1<x<2