Question

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

giai bpt

Answer 1

Ta có : \(\frac{x}{x-3}>1\) ( ĐKXĐ : \(x\ne3\) )

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

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

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

\(\Leftrightarrow x-3>0\)

\(\Leftrightarrow x>3\)

Vậy : \(x>3\) thỏa mãn đề.

Answer 2

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

<=> \(\frac{3}{x-3}>0\)

Vì 3 > 0 nên để \(\frac{3}{x-3}>0\) thì x - 3 > 0 <=> x > 3

Answer 3

\(\frac{x}{x-3}>1\left(x\ne3\right)\)

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

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

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

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

Vì 3>0 => Để \(\frac{3}{x-3}\)> 0 thì x-3 >0 

=> x>3

Vậy để \(\frac{x}{x-3}>1\)thì x>3