Question

giải pt sau:x/x+1-1/x-2=3x-11/(x+1).(x-2)

Answer 1

\(\dfrac{x}{x+1}-\dfrac{1}{x-2}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\)

ĐKXĐ : \(\left\{{}\begin{matrix}x+1\ne0\\x-2\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne-1\\x\ne2\end{matrix}\right.\)

Ta có : \(\dfrac{x}{x+1}-\dfrac{1}{x-2}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\)

\(\Leftrightarrow\dfrac{x\left(x-2\right)}{\left(x+1\right)\left(x-2\right)}-\dfrac{x+1}{\left(x+1\right)\left(x-2\right)}=\dfrac{3x-11}{\left(x+1\right)\left(x-2\right)}\)

`=> x^2 -2x -(x+1)=3x-11`

`<=> x^2 -2x - x-1-3x+11=0`

`<=> x^2 -6x+10=0`

Bạn ơi đề như thế ạ chứ mình làm ko ra ạ .