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

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

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((x^2-5)(x^2-4))/((x-1))<0

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

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

Interval Notation

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

Decimal

x < - 2.23606 \dots or - 2 < x < 1 or 2 < x < 2.23606 \dots

Solution steps

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

Factor

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

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

Identify the intervals

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

3 x^{2} - 8 x + 2 < 0

x (x - 1) (x - 2) (x - 3) > 0

x^{5} - 7 x^{4} + 13 x^{3} - x^{2} - 14 x + 8 \leq 0

\frac{x}{( x ^{2} - 3 x - 4 )} > 0

\frac{1}{( x + 1 )} - \frac{1}{x} \leq \frac{1}{( x - 1 )} - \frac{1}{( x - 2 )}

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