What is (((x-7-x^2)(x^2+6)))/((x^2-x-1))<= 0 ?

The solution to (((x-7-x^2)(x^2+6)))/((x^2-x-1)) (1+sqrt(5))/2

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(((x-7-x^2)(x^2+6)))/((x^2-x-1))<= 0

\frac{( ( x - 7 - x ^{2} ) ( x ^{2} + 6 ) )}{( x ^{2} - x - 1 )} \leq 0

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

Interval Notation

(- \infty, \frac{1 - 5}{2}) \cup (\frac{1 + 5}{2}, \infty)

Decimal Notation

x < - 0.61803 \dots or x > 1.61803 \dots

Solution steps

\frac{( x - 7 - x ^{2} ) ( x ^{2} + 6 )}{x ^{2} - x - 1} \leq 0

Factor

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

\frac{( - ( - x + 7 + x ^{2} ) ) ( x ^{2} + 6 )}{( x - \frac{1 + 5}{2} ) ( x - \frac{1 - 5}{2} )} \leq 0

Identify the intervals

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

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

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

x^{3} + x^{3} - x - 1 > 0

(x^{2} - 4) (x^{2} - 9) \geq 0

m^{2} =< \frac{2}{3}

What is (((x-7-x^2)(x^2+6)))/((x^2-x-1))<= 0 ?
The solution to (((x-7-x^2)(x^2+6)))/((x^2-x-1))<= 0 is x<(1-sqrt(5))/2 \lor x>(1+sqrt(5))/2