1/((x-2))+1/((x-1))> 1/x

Lösung

\frac{1}{( x - 2 )} + \frac{1}{( x - 1 )} > \frac{1}{x}

- 2 < x < 0 or 1 < x < 2 or x > 2

Intervall-Notation

(- 2, 0) \cup (1, 2) \cup (2, \infty)

Dezimale

- 1.41421 \dots < x < 0 or 1 < x < 1.41421 \dots or x > 2

Schritte zur Lösung

\frac{1}{x - 2} + \frac{1}{x - 1} > \frac{1}{x}

Rewrite in standard form

\frac{x ^{2} - 2}{x ( x - 2 ) ( x - 1 )} > 0

Faktorisiere

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

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

Identifiziere die Intervalle

- 2 < x < 0 or 1 < x < 2 or x > 2

so l v e f or h, h_{2} \cdot s + s \cdot o_{2} - > h_{2} \cdot o + s

(x - 1) (2 x - 5) < 0

- 1 < \frac{1}{x}

\frac{( x - 1 )}{( 2 - x )} > 0

v^{2} > v^{1}