(((x-2)^2*(x-4)^4))/((x^2-x+1))<= 0

Lösung

\frac{( ( x - 2 ) ^{2} \cdot ( x - 4 ) ^{4} )}{( x ^{2} - x + 1 )} \leq 0

x = 2 or x = 4

Intervall-Notation

x = 2 \cup x = 4

Schritte zur Lösung

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

Rewrite in standard form

\frac{( 24 x ^{4} + 2304 x ^{2} + 4 ( - 96 x ^{3} - 1536 x ) + 6144 ) ( x - 2 ) ^{2}}{x ^{2} - x + 1} \leq 0

Faktor

\frac{( 24 x ^{4} + 2304 x ^{2} + 4 ( - 96 x ^{3} - 1536 x ) + 6144 ) ( x - 2 ) ^{2}}{x ^{2} - x + 1} : \frac{24 ( x - 4 ) ^{4} ( x - 2 ) ^{2}}{x ^{2} - x + 1}

\frac{24 ( x - 4 ) ^{4} ( x - 2 ) ^{2}}{x ^{2} - x + 1} \leq 0

Teile beide Seiten durch

24

\frac{\frac{24 ( x - 4 ) ^{4} ( x - 2 ) ^{2}}{x ^{2} - x + 1}}{24} \leq \frac{0}{24}

Vereinfache

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

Identifiziere die Intervalle

x = 2, x = 4

x = 2 or x = 4

x (x^{2} + 1) \geq 2

\frac{( x ^{2} + 7 x + 10 )}{( x ^{2} - 4 )} \geq 0

6 x^{3} + x^{2} - 54 x + 56 < 0

\frac{x}{( x - 3 )} < \frac{9}{( 4 x + 3 )}

\frac{( x - 4 )}{( x + 2 )} \geq \frac{( x - 5 )}{( x + 4 )}