(x+3)/(x^2-4)-1/(x+2)<(2x)/(2x-x^2)

Lösung

\frac{x + 3}{x ^{2} - 4} - \frac{1}{x + 2} < \frac{2 x}{2 x - x ^{2}}

x < - \frac{9}{2} or - 2 < x < 0 or 0 < x < 2

Intervall-Notation

(- \infty, - \frac{9}{2}) \cup (- 2, 0) \cup (0, 2)

Dezimale

x < - 4.5 or - 2 < x < 0 or 0 < x < 2

Schritte zur Lösung

\frac{x + 3}{x ^{2} - 4} - \frac{1}{x + 2} < \frac{2 x}{2 x - x ^{2}}

Rewrite in standard form

\frac{2 x ^{2} + 9 x}{x ( x + 2 ) ( x - 2 )} < 0

Faktorisiere

\frac{2 x ^{2} + 9 x}{x ( x + 2 ) ( x - 2 )} : \frac{x ( 2 x + 9 )}{x ( x + 2 ) ( x - 2 )}

\frac{x ( 2 x + 9 )}{x ( x + 2 ) ( x - 2 )} < 0

Identifiziere die Intervalle

x < - \frac{9}{2} or - 2 < x < 0 or 0 < x < 2

3 - 3 x^{2} = 0

24 > 4 w

f a c t or 2 r^{2} - 3 r + 1

s im pl i f y \frac{0}{- 4}

\frac{7 - x}{x - 4} > 0