((x^3+1))/((x^4+x^3-10x^2-13x+21))>0

Lösung

\frac{( x ^{3} + 1 )}{( x ^{4} + x ^{3} - 10 x ^{2} - 13 x + 21 )} > 0

- 1 < x < 1 or x > 3

Intervall-Notation

(- 1, 1) \cup (3, \infty)

Schritte zur Lösung

\frac{x ^{3} + 1}{x ^{4} + x ^{3} - 10 x ^{2} - 13 x + 21} > 0

Faktor

\frac{x ^{3} + 1}{x ^{4} + x ^{3} - 10 x ^{2} - 13 x + 21} : \frac{( x + 1 ) ( x ^{2} - x + 1 )}{( x - 1 ) ( x - 3 ) ( x ^{2} + 5 x + 7 )}

\frac{( x + 1 ) ( x ^{2} - x + 1 )}{( x - 1 ) ( x - 3 ) ( x ^{2} + 5 x + 7 )} > 0

Identifiziere die Intervalle

- 1 < x < 1 or x > 3

(x + 1) (x^{2} + x - 1) < (x + 1)

(x - 1)^{2} \cdot (x + 1)^{3} \cdot (x - 4) \geq 0

4 x^{3} - 3 x^{2} - 16 x + 12 < 0

\frac{( m + 1 )}{m} \leq 0

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