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

Lösung

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

- \frac{3}{2} < x < 0 or \frac{1}{2} < x < 4

Intervall-Notation

(- \frac{3}{2}, 0) \cup (\frac{1}{2}, 4)

Dezimale

- 1.5 < x < 0 or 0.5 < x < 4

Schritte zur Lösung

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

Faktorisiere

\frac{( 2 x + 1 ) ^{2} - 4}{x ^{2} - 4 x} : \frac{( 2 x - 1 ) ( 2 x + 3 )}{x ( x - 4 )}

\frac{( 2 x - 1 ) ( 2 x + 3 )}{x ( x - 4 )} < 0

Identifiziere die Intervalle

- \frac{3}{2} < x < 0 or \frac{1}{2} < x < 4

(x - 1)^{4} \cdot (x - 3)^{6} \cdot (x - 2)^{5} \cdot (x - 4)^{10} > 0

\frac{1}{( x - 5 )} < 3

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

(x - 1) (x - 5) (x - 15) \leq 0, (x - 3) (x - 10) > 0

[x + 6] > 4