((5+x))/((12-3x-x^2))>=-2

Lösung

\frac{( 5 + x )}{( 12 - 3 x - x ^{2} )} \geq - 2

x < \frac{- 3 - 57}{2} or \frac{- 5 - 257}{4} \leq x < \frac{57 - 3}{2} or x \geq \frac{257 - 5}{4}

Intervall-Notation

(- \infty, \frac{- 3 - 57}{2}) \cup [\frac{- 5 - 257}{4}, \frac{57 - 3}{2}) \cup [\frac{257 - 5}{4}, \infty)

Dezimale

x < - 5.27491 \dots or - 5.25780 \dots \leq x < 2.27491 \dots or x \geq 2.75780 \dots

Schritte zur Lösung

\frac{5 + x}{12 - 3 x - x ^{2}} \geq - 2

Rewrite in standard form

\frac{- 2 x ^{2} - 5 x + 29}{12 - 3 x - x ^{2}} \geq 0

Faktor

- 2 x^{2} - 5 x + 29 : - (x - \frac{- 5 + 257}{4}) (x - \frac{- 5 - 257}{4})

\frac{- ( x - \frac{- 5 + 257}{4} ) ( x - \frac{- 5 - 257}{4} )}{12 - 3 x - x ^{2}} \geq 0

Faktor

12 - 3 x - x^{2} : - (x - \frac{- 3 + 57}{2}) (x - \frac{- 3 - 57}{2})

\frac{- ( x - \frac{- 5 + 257}{4} ) ( x - \frac{- 5 - 257}{4} )}{- ( x - \frac{- 3 + 57}{2} ) ( x - \frac{- 3 - 57}{2} )} \geq 0

Vereinfache

\frac{( x - \frac{- 5 + 257}{4} ) ( x - \frac{- 5 - 257}{4} )}{( x - \frac{- 3 + 57}{2} ) ( x - \frac{- 3 - 57}{2} )}

Identifiziere die Intervalle

x < \frac{- 3 - 57}{2} or \frac{- 5 - 257}{4} \leq x < \frac{57 - 3}{2} or x \geq \frac{257 - 5}{4}

- x^{2} + x + 6 > 0

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

\frac{( x + 2 )}{( x - 2 )} > 0

\frac{1}{x} > \frac{1}{( x - 1 )}

(x - 3) (x - 2) \geq 0