Question

Giải bất phương trình: (x-1)/(x-3)>1

Answer 1

    \(\dfrac{x-1}{x-3}>1\)

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

⇔ `x-1>x-3`

⇔ x-x>1-3

⇔ 0x>-2 (luôn đúng)

 Vậy ....

Answer 2

ĐKXĐ \(x\ne3\)

\(\dfrac{x-1}{x-3}>1\Leftrightarrow\dfrac{x-1}{x-3}-1>0\Leftrightarrow\dfrac{x-1-x+3}{x-3}>0\Leftrightarrow\dfrac{2}{x-3}>0\Leftrightarrow x-3>0\Leftrightarrow x>3\)

Vậy, x > 3 thì bpt thỏa mãn

Answer 3

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

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

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

\(\dfrac{2}{x-3}>0\) (tử mẫu cùng dấu) mà 2>0

=>x-3>0

x>3