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

The solution to (((x^2-3x+1)^3))/(((x-1)(x+2)))<= 0 is -2<x<= (3-sqrt(5))/2 \lor 1<x<= (3+sqrt(5))/2

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

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

- 2 < x \leq \frac{3 - 5}{2} or 1 < x \leq \frac{3 + 5}{2}

Interval Notation

(- 2, \frac{3 - 5}{2}] \cup (1, \frac{3 + 5}{2}]

Decimal Notation

- 2 < x \leq 0.38196 \dots or 1 < x \leq 2.61803 \dots

Solution steps

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

Identify the intervals

- 2 < x \leq \frac{3 - 5}{2} or 1 < x \leq \frac{3 + 5}{2}

x^{4} - 2 x^{3} - x + 2 > 0

x^{2} - 3 x + 5 > 0

(x + 4)^{5} \cdot (x + 3)^{6} \cdot (x + 2)^{7} \cdot (x - 1)^{8} \leq 0

2 x < 3 - x^{2}

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

What is (((x^2-3x+1)^3))/(((x-1)(x+2)))<= 0 ?
The solution to (((x^2-3x+1)^3))/(((x-1)(x+2)))<= 0 is -2<x<= (3-sqrt(5))/2 \lor 1<x<= (3+sqrt(5))/2