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

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

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

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

- 1 < x < 1 or 1 < x < 4

Interval Notation

(- 1, 1) \cup (1, 4)

Solution steps

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

Identify the intervals

- 1 < x < 1 or 1 < x < 4

- x^{2} + x + 1 \leq 0

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

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

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

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

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