Question

\(\frac{x-1}{x-3}\) > 1

giúp mình nhanh với

Answer 1

\(\Leftrightarrow\frac{x-1}{x-3}-1>0\Leftrightarrow\frac{x-1-x+3}{x-3}>0\)

\(\Leftrightarrow\frac{2}{x-3}>0\Rightarrow x-3>0\Rightarrow x>3\)

Answer 2

\(\frac{x-1}{x-3}>1\)

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

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

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

\(\Leftrightarrow\frac{2}{\frac{x-3}{2}}>\frac{0}{2}\)

\(\Leftrightarrow\frac{1}{x-3}>0\)

=> x > 3