Sprawdzenie nierównosci
: 6 sie 2010, o 16:37
Proszę o sprawdzenie tej nierówności:
\(\displaystyle{ \frac{2}{x-1}< \frac{3}{x}}\)
\(\displaystyle{ \frac{2}{x-1}- \frac{3}{x}<0}\)
\(\displaystyle{ \frac{2x-3(x-1)}{x(x-1)} <0}\)
\(\displaystyle{ \frac{-x-3}{x(x-1)}<0}\)
\(\displaystyle{ (-x-3)x(x-1)<0}\)
\(\displaystyle{ x \in (-3,0) \cup (1,+ \infty)}\)
\(\displaystyle{ \frac{2}{x-1}< \frac{3}{x}}\)
\(\displaystyle{ \frac{2}{x-1}- \frac{3}{x}<0}\)
\(\displaystyle{ \frac{2x-3(x-1)}{x(x-1)} <0}\)
\(\displaystyle{ \frac{-x-3}{x(x-1)}<0}\)
\(\displaystyle{ (-x-3)x(x-1)<0}\)
\(\displaystyle{ x \in (-3,0) \cup (1,+ \infty)}\)