Question

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

Answer 1

 

x −1x−3>1

 

 

x−1x−3- 1 >0

 

x−1x−3- \(\dfrac{\text{x − 3}}{\text{x − 3}}\) > 0

 

\(\dfrac{-4}{\text{x − 3}}\) > 0

=> -4 và x-3 khác dấu

mà  -4 <0

=> x-3 > 0

=> x . 3

 

 

 

x−1x−3>1

 

 

Answer 2

Ta có: \(\dfrac{x-1}{x-3}>1\)

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

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

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

mà 2>0

nên x-3>0

hay x>3