What is ((x^2*(x-2)(5-x)))/(((x^2-4)(x-1)))>0 ?

The solution to ((x^2*(x-2)(5-x)))/(((x^2-4)(x-1)))>0 is x<-2\lor 1<x<2\lor 2<x<5

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((x^2*(x-2)(5-x)))/(((x^2-4)(x-1)))>0

\frac{( x ^{2} \cdot ( x - 2 ) ( 5 - x ) )}{( ( x ^{2} - 4 ) ( x - 1 ) )} > 0

x < - 2 or 1 < x < 2 or 2 < x < 5

Interval Notation

(- \infty, - 2) \cup (1, 2) \cup (2, 5)

Solution steps

\frac{x ^{2} ( x - 2 ) ( 5 - x )}{( x ^{2} - 4 ) ( x - 1 )} > 0

Factor

\frac{x ^{2} ( x - 2 ) ( 5 - x )}{( x ^{2} - 4 ) ( x - 1 )} : \frac{x ^{2} ( x - 2 ) ( 5 - x )}{( x + 2 ) ( x - 2 ) ( x - 1 )}

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

Identify the intervals

x < - 2 or 1 < x < 2 or 2 < x < 5

\frac{( 6 x - x ^{2} )}{( ( x + 9 ) ^{2} )} \leq 0

\frac{2}{3 x} > - 6 x

\frac{( x + 1 ) ( x - 1 ) ( x + 2 )}{( x ^{2} + 3 x + 2 ) ( x + 5 )} \leq 0

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

\frac{( 2 x + 1 )}{( 3 x - 6 )} \geq 3

What is ((x^2*(x-2)(5-x)))/(((x^2-4)(x-1)))>0 ?
The solution to ((x^2*(x-2)(5-x)))/(((x^2-4)(x-1)))>0 is x<-2\lor 1<x<2\lor 2<x<5